1	1	1	1
2	2	1+2 z	2 z
2	11	1	2
11	11	2+2 z	2+2 z
3	3	1+6 z+6 z^2	6 z^2
3	21	2+6 z	12 z
3	111	1	6
21	21	2+7 z+3 z^2	1+8 z+3 z^2
21	111	2+4 z	4+8 z
111	111	6+18 z+6 z^2	6+24 z+6 z^2
4	4	1+12 z+36 z^2+24 z^3	24 z^3
4	31	3+24 z+36 z^2	72 z^2
4	22	2+12 z+12 z^2	24 z+24 z^2
4	211	3+12 z	72 z
4	1111	1	24
31	31	2+16 z+28 z^2+8 z^3	8 z+32 z^2+8 z^3
31	22	2+12 z+12 z^2	24 z+24 z^2
31	211	4+22 z+20 z^2	4+52 z+40 z^2
31	1111	2+6 z	12+36 z
22	22	4+30 z+48 z^2+12 z^3	24 z+60 z^2+12 z^3
22	211	4+22 z+20 z^2	4+52 z+40 z^2
22	1111	4+18 z+12 z^2	12+60 z+24 z^2
211	211	6+38 z+48 z^2+8 z^3	4+60 z+72 z^2+8 z^3
211	1111	6+30 z+24 z^2	12+84 z+48 z^2
1111	1111	24+144 z+168 z^2+24 z^3	24+264 z+264 z^2+24 z^3
5	5	1+20 z+120 z^2+240 z^3+120 z^4	120 z^4
5	41	4+60 z+240 z^2+240 z^3	480 z^3
5	32	5+60 z+180 z^2+120 z^3	360 z^2+240 z^3
5	311	6+60 z+120 z^2	720 z^2
5	221	5+40 z+60 z^2	240 z+360 z^2
5	2111	4+20 z	480 z
5	11111	1	120
41	41	2+29 z+117 z^2+138 z^3+30 z^4	54 z^2+156 z^3+30 z^4
41	32	4+46 z+132 z^2+84 z^3	24 z+288 z^2+168 z^3
41	311	6+66 z+180 z^2+108 z^3	72 z+432 z^2+216 z^3
41	221	6+54 z+108 z^2+36 z^3	216 z+432 z^2+72 z^3
41	2111	6+45 z+63 z^2	18+324 z+378 z^2
41	11111	2+8 z	48+192 z
32	32	4+50 z+168 z^2+156 z^3+24 z^4	24 z+216 z^2+216 z^3+24 z^4
32	311	4+42 z+108 z^2+60 z^3	72 z+288 z^2+120 z^3
32	221	8+80 z+194 z^2+100 z^3	4+192 z+564 z^2+200 z^3
32	2111	8+68 z+128 z^2+40 z^3	16+336 z+528 z^2+80 z^3
32	11111	4+26 z+30 z^2	36+264 z+180 z^2
311	311	6+70 z+214 z^2+172 z^3+20 z^4	64 z+372 z^2+264 z^3+20 z^4
311	221	6+58 z+134 z^2+64 z^3	4+168 z+420 z^2+128 z^3
311	2111	12+112 z+248 z^2+112 z^3	16+384 z+816 z^2+224 z^3
311	11111	6+42 z+54 z^2	36+360 z+324 z^2
221	221	12+130 z+362 z^2+256 z^3+24 z^4	4+216 z+780 z^2+416 z^3+24 z^4
221	2111	12+112 z+248 z^2+112 z^3	16+384 z+816 z^2+224 z^3
221	11111	12+102 z+198 z^2+72 z^3	36+504 z+756 z^2+144 z^3
2111	2111	24+246 z+636 z^2+402 z^3+30 z^4	18+564 z+1584 z^2+684 z^3+30 z^4
2111	11111	24+216 z+456 z^2+192 z^3	48+864 z+1584 z^2+384 z^3
11111	11111	120+1200 z+3000 z^2+1800 z^3+120 z^4	120+3120 z+7920 z^2+3120 z^3+120 z^4
6	6	1+30 z+300 z^2+1200 z^3+1800 z^4+720 z^5	720 z^5
6	51	5+120 z+900 z^2+2400 z^3+1800 z^4	3600 z^4
6	42	9+180 z+1080 z^2+2160 z^3+1080 z^4	4320 z^3+2160 z^4
6	411	10+180 z+900 z^2+1200 z^3	7200 z^3
6	33	5+90 z+480 z^2+840 z^3+360 z^4	720 z^2+2160 z^3+720 z^4
6	321	16+240 z+960 z^2+960 z^3	5760 z^2+5760 z^3
6	3111	10+120 z+300 z^2	7200 z^2
6	222	5+60 z+180 z^2+120 z^3	720 z+2160 z^2+720 z^3
6	2211	9+90 z+180 z^2	2160 z+4320 z^2
6	21111	5+30 z	3600 z
6	111111	1	720
51	51	2+46 z+336 z^2+912 z^3+816 z^4+144 z^5	384 z^3+912 z^4+144 z^5
51	42	6+114 z+648 z^2+1224 z^3+576 z^4	432 z^2+2736 z^3+1152 z^4
51	411	8+148 z+816 z^2+1488 z^3+672 z^4	864 z^2+3552 z^3+1344 z^4
51	33	4+68 z+336 z^2+528 z^3+192 z^4	864 z^2+1632 z^3+384 z^4
51	321	16+248 z+1080 z^2+1392 z^3+336 z^4	288 z+4896 z^2+5664 z^3+672 z^4
51	3111	12+168 z+624 z^2+576 z^3	576 z+4608 z^2+3456 z^3
51	222	6+78 z+264 z^2+216 z^3	576 z+2448 z^2+1296 z^3
51	2211	12+144 z+432 z^2+288 z^3	1728 z+5184 z^2+1728 z^3
51	21111	8+76 z+144 z^2	96+2208 z+3456 z^2
51	111111	2+10 z	240+1200 z
42	42	4+78 z+470 z^2+1012 z^3+676 z^4+80 z^5	8 z+376 z^2+1464 z^3+952 z^4+80 z^5
42	411	4+70 z+362 z^2+612 z^3+252 z^4	24 z+696 z^2+1656 z^3+504 z^4
42	33	4+70 z+362 z^2+612 z^3+252 z^4	24 z+696 z^2+1656 z^3+504 z^4
42	321	16+256 z+1184 z^2+1728 z^3+576 z^4	384 z+4224 z^2+5760 z^3+1152 z^4
42	3111	12+174 z+702 z^2+828 z^3+180 z^4	648 z+4104 z^2+3528 z^3+360 z^4
42	222	8+116 z+478 z^2+612 z^3+180 z^4	552 z+2616 z^2+2232 z^3+360 z^4
42	2211	16+212 z+750 z^2+696 z^3+60 z^4	24+1488 z+6192 z^2+3696 z^3+120 z^4
42	21111	12+138 z+396 z^2+252 z^3	72+2088 z+4968 z^2+1512 z^3
42	111111	4+34 z+56 z^2	144+1392 z+1344 z^2
411	411	6+114 z+660 z^2+1332 z^3+792 z^4+72 z^5	648 z^2+2376 z^3+1224 z^4+72 z^5
411	321	12+192 z+888 z^2+1296 z^3+432 z^4	288 z+3168 z^2+4320 z^3+864 z^4
411	3111	18+282 z+1272 z^2+1800 z^3+576 z^4	576 z+5040 z^2+6192 z^3+1152 z^4
411	222	6+78 z+264 z^2+216 z^3	576 z+2448 z^2+1296 z^3
411	2211	18+246 z+924 z^2+996 z^3+192 z^4	24+1560 z+6552 z^2+4440 z^3+384 z^4
411	21111	18+222 z+708 z^2+540 z^3	72+2376 z+7272 z^2+3240 z^3
411	111111	6+54 z+96 z^2	144+1872 z+2304 z^2
33	33	8+156 z+936 z^2+1992 z^3+1296 z^4+144 z^5	720 z^2+3024 z^3+1872 z^4+144 z^5
33	321	16+264 z+1272 z^2+1968 z^3+720 z^4	288 z+3744 z^2+6048 z^3+1440 z^4
33	3111	8+108 z+384 z^2+336 z^3	576 z+3168 z^2+2016 z^3
33	222	8+108 z+384 z^2+336 z^3	576 z+3168 z^2+2016 z^3
33	2211	24+348 z+1428 z^2+1788 z^3+480 z^4	24+1560 z+7848 z^2+6888 z^3+960 z^4
33	21111	16+192 z+588 z^2+420 z^3	72+2376 z+6552 z^2+2520 z^3
33	111111	8+84 z+216 z^2+120 z^3	144+1872 z+3024 z^2+720 z^3
321	321	12+200 z+991 z^2+1648 z^3+755 z^4+45 z^5	1+281 z+2730 z^2+4298 z^3+1285 z^4+45 z^5
321	3111	12+182 z+790 z^2+1066 z^3+320 z^4	4+548 z+3612 z^2+3836 z^3+640 z^4
321	222	12+182 z+790 z^2+1066 z^3+320 z^4	4+548 z+3612 z^2+3836 z^3+640 z^4
321	2211	24+348 z+1428 z^2+1788 z^3+480 z^4	24+1560 z+7848 z^2+6888 z^3+960 z^4
321	21111	24+320 z+1168 z^2+1216 z^3+224 z^4	64+2432 z+8832 z^2+5504 z^3+448 z^4
321	111111	12+138 z+402 z^2+270 z^3	108+2124 z+4788 z^2+1620 z^3
3111	3111	24+396 z+1932 z^2+3132 z^3+1368 z^4+72 z^5	576 z+5688 z^2+8568 z^3+2376 z^4+72 z^5
3111	2211	24+348 z+1428 z^2+1788 z^3+480 z^4	24+1560 z+7848 z^2+6888 z^3+960 z^4
3111	21111	48+684 z+2748 z^2+3348 z^3+864 z^4	72+3528 z+16056 z^2+13176 z^3+1728 z^4
3111	111111	24+288 z+888 z^2+648 z^3	144+3600 z+9648 z^2+3888 z^3
222	222	36+606 z+3036 z^2+5112 z^3+2376 z^4+144 z^5	720 z+7920 z^2+13104 z^3+4032 z^4+144 z^5
222	2211	36+534 z+2256 z^2+2940 z^3+840 z^4	24+1992 z+11304 z^2+10920 z^3+1680 z^4
222	21111	36+498 z+1920 z^2+2196 z^3+504 z^4	72+3096 z+12600 z^2+9144 z^3+1008 z^4
222	111111	36+474 z+1716 z^2+1800 z^3+360 z^4	144+4032 z+13104 z^2+7920 z^3+720 z^4
2211	2211	48+748 z+3404 z^2+5044 z^3+1936 z^4+80 z^5	24+2072 z+13336 z^2+15576 z^3+3472 z^4+80 z^5
2211	21111	48+684 z+2748 z^2+3348 z^3+864 z^4	72+3528 z+16056 z^2+13176 z^3+1728 z^4
2211	111111	48+648 z+2424 z^2+2664 z^3+576 z^4	144+4752 z+17136 z^2+11376 z^3+1152 z^4
21111	21111	120+1824 z+8040 z^2+11400 z^3+4080 z^4+144 z^5	96+6240 z+35280 z^2+37200 z^3+7440 z^4+144 z^5
21111	111111	120+1680 z+6600 z^2+7800 z^3+1920 z^4	240+9840 z+41040 z^2+31440 z^3+3840 z^4
111111	111111	720+10800 z+46800 z^2+64800 z^3+22320 z^4+720 z^5	720+41040 z+217440 z^2+217440 z^3+41040 z^4+720 z^5
7	7	1+42 z+630 z^2+4200 z^3+12600 z^4+15120 z^5+5040 z^6	5040 z^6
7	61	6+210 z+2520 z^2+12600 z^3+25200 z^4+15120 z^5	30240 z^5
7	52	14+420 z+4200 z^2+16800 z^3+25200 z^4+10080 z^5	50400 z^4+20160 z^5
7	511	15+420 z+3780 z^2+12600 z^3+12600 z^4	75600 z^4
7	43	14+378 z+3360 z^2+11760 z^3+15120 z^4+5040 z^5	20160 z^3+40320 z^4+10080 z^5
7	421	35+840 z+6300 z^2+16800 z^3+12600 z^4	100800 z^3+75600 z^4
7	4111	20+420 z+2520 z^2+4200 z^3	100800 z^3
7	331	21+462 z+3150 z^2+7560 z^3+5040 z^4	15120 z^2+60480 z^3+30240 z^4
7	322	21+420 z+2520 z^2+5040 z^3+2520 z^4	30240 z^2+60480 z^3+15120 z^4
7	3211	35+630 z+3150 z^2+4200 z^3	75600 z^2+100800 z^3
7	31111	15+210 z+630 z^2	75600 z^2
7	2221	14+210 z+840 z^2+840 z^3	10080 z+40320 z^2+20160 z^3
7	22111	14+168 z+420 z^2	20160 z+50400 z^2
7	211111	6+42 z	30240 z
7	1111111	1	5040
61	61	2+67 z+775 z^2+3800 z^3+7800 z^4+5640 z^5+840 z^6	3000 z^4+6240 z^5+840 z^6
61	52	8+228 z+2160 z^2+8160 z^3+11520 z^4+4320 z^5	5760 z^3+25920 z^4+8640 z^5
61	511	10+280 z+2600 z^2+9600 z^3+13200 z^4+4800 z^5	9600 z^3+31200 z^4+9600 z^5
61	43	10+255 z+2115 z^2+6780 z^3+7740 z^4+2160 z^5	1080 z^2+20160 z^3+24840 z^4+4320 z^5
61	421	30+720 z+5520 z^2+15840 z^3+15120 z^4+2880 z^5	8640 z^2+74880 z^3+61920 z^4+5760 z^5
61	4111	20+450 z+3150 z^2+7800 z^3+5400 z^4	10800 z^2+57600 z^3+32400 z^4
61	331	20+440 z+3040 z^2+7680 z^3+6240 z^4+960 z^5	17280 z^2+53760 z^3+27840 z^4+1920 z^5
61	322	22+452 z+2840 z^2+6160 z^3+3600 z^4	960 z+26880 z^2+61440 z^3+21600 z^4
61	3211	40+780 z+4560 z^2+8880 z^3+4320 z^4	2880 z+63360 z^2+109440 z^3+25920 z^4
61	31111	20+340 z+1600 z^2+2000 z^3	4800 z+48000 z^2+48000 z^3
61	2221	18+303 z+1455 z^2+2100 z^3+540 z^4	7200 z+42840 z^2+37440 z^3+3240 z^4
61	22111	20+300 z+1200 z^2+1200 z^3	14400 z+57600 z^2+28800 z^3
61	211111	10+115 z+275 z^2	600+16800 z+33000 z^2
61	1111111	2+12 z	1440+8640 z
52	52	4+114 z+1098 z^2+4356 z^3+6948 z^4+3672 z^5+360 z^6	216 z^2+4032 z^3+10368 z^4+5184 z^5+360 z^6
52	511	4+106 z+926 z^2+3192 z^3+4056 z^4+1344 z^5	432 z^2+6144 z^3+10896 z^4+2688 z^5
52	43	8+204 z+1704 z^2+5568 z^3+6624 z^4+2016 z^5	1728 z^2+14976 z^3+19584 z^4+4032 z^5
52	421	24+576 z+4470 z^2+13308 z^3+13968 z^4+3528 z^5	144 z+10512 z^2+54720 z^3+48528 z^4+7056 z^5
52	4111	16+360 z+2568 z^2+6792 z^3+5904 z^4+1008 z^5	288 z+11520 z^2+41472 z^3+25344 z^4+2016 z^5
52	331	20+446 z+3148 z^2+8220 z^3+7032 z^4+1176 z^5	432 z+15552 z^2+52032 z^3+30432 z^4+2352 z^5
52	322	24+516 z+3510 z^2+8892 z^3+7632 z^4+1512 z^5	1296 z+25488 z^2+60480 z^3+30672 z^4+3024 z^5
52	3211	44+894 z+5592 z^2+12300 z^3+7848 z^4+504 z^5	3888 z+57888 z^2+116928 z^3+42048 z^4+1008 z^5
52	31111	24+444 z+2448 z^2+4464 z^3+2016 z^4	5184 z+44928 z^2+58752 z^3+12096 z^4
52	2221	24+444 z+2472 z^2+4656 z^3+2304 z^4	6336 z+44352 z^2+56448 z^3+13824 z^4
52	22111	28+474 z+2310 z^2+3456 z^3+1008 z^4	144+11520 z+64656 z^2+58752 z^3+6048 z^4
52	211111	16+232 z+896 z^2+864 z^3	384+14208 z+45312 z^2+20736 z^3
52	1111111	4+42 z+90 z^2	720+8640 z+10800 z^2
511	511	6+170 z+1614 z^2+6224 z^3+9408 z^4+4464 z^5+336 z^6	6144 z^3+16848 z^4+6912 z^5+336 z^6
511	421	18+438 z+3450 z^2+10440 z^3+11160 z^4+2880 z^5	6480 z^2+40320 z^3+38160 z^4+5760 z^5
511	4111	24+576 z+4464 z^2+13248 z^3+13824 z^4+3456 z^5	10368 z^2+55296 z^3+48384 z^4+6912 z^5
511	331	12+268 z+1908 z^2+5104 z^3+4656 z^4+960 z^5	384 z+9888 z^2+29952 z^3+18336 z^4+1920 z^5
511	322	18+366 z+2274 z^2+4872 z^3+2808 z^4	1152 z+23184 z^2+49536 z^3+16848 z^4
511	3211	48+1008 z+6624 z^2+15840 z^3+12096 z^4+1728 z^5	3456 z+55296 z^2+124416 z^3+55296 z^4+3456 z^5
511	31111	36+708 z+4236 z^2+8688 z^3+4752 z^4	4608 z+53856 z^2+94464 z^3+28512 z^4
511	2221	24+432 z+2304 z^2+4032 z^3+1728 z^4	6912 z+48384 z^2+55296 z^3+10368 z^4
511	22111	36+636 z+3324 z^2+5688 z^3+2376 z^4	144+12672 z+74880 z^2+79488 z^3+14256 z^4
511	211111	24+368 z+1536 z^2+1664 z^3	384+16128 z+64512 z^2+39936 z^3
511	1111111	6+66 z+150 z^2	720+11520 z+18000 z^2
43	43	8+216 z+1950 z^2+7140 z^3+10260 z^4+4680 z^5+360 z^6	1080 z^2+11520 z^3+20160 z^4+7200 z^5+360 z^6
43	421	16+384 z+2988 z^2+8964 z^3+9576 z^4+2520 z^5	144 z+7488 z^2+35712 z^3+32256 z^4+5040 z^5
43	4111	8+168 z+1086 z^2+2448 z^3+1512 z^4	288 z+8496 z^2+22464 z^3+9072 z^4
43	331	24+564 z+4284 z^2+12492 z^3+12888 z^4+3240 z^5	432 z+13824 z^2+55296 z^3+44928 z^4+6480 z^5
43	322	24+516 z+3492 z^2+8676 z^3+6984 z^4+1080 z^5	1296 z+24192 z^2+62208 z^3+31104 z^4+2160 z^5
43	3211	48+1008 z+6636 z^2+15948 z^3+12312 z^4+1800 z^5	3888 z+55296 z^2+123264 z^3+55872 z^4+3600 z^5
43	31111	24+444 z+2448 z^2+4464 z^3+2016 z^4	5184 z+44928 z^2+58752 z^3+12096 z^4
43	2221	32+624 z+3756 z^2+8082 z^3+5454 z^4+720 z^5	36+6048 z+50760 z^2+77472 z^3+25524 z^4+1440 z^5
43	22111	40+732 z+4020 z^2+7416 z^3+3528 z^4	144+11520 z+75456 z^2+93312 z^3+21168 z^4
43	211111	24+384 z+1746 z^2+2394 z^3+630 z^4	324+14688 z+59832 z^2+42336 z^3+3780 z^4
43	1111111	8+108 z+384 z^2+336 z^3	576+9792 z+21888 z^2+8064 z^3
421	421	12+294 z+2364 z^2+7500 z^3+8928 z^4+3096 z^5+144 z^6	144 z+5328 z^2+24768 z^3+24768 z^4+5328 z^5+144 z^6
421	4111	12+276 z+2040 z^2+5736 z^3+5616 z^4+1296 z^5	288 z+8064 z^2+28800 z^3+20736 z^4+2592 z^5
421	331	12+270 z+1944 z^2+5292 z^3+4968 z^4+1080 z^5	432 z+9504 z^2+29376 z^3+19008 z^4+2160 z^5
421	322	24+528 z+3702 z^2+9756 z^3+8784 z^4+1800 z^5	1296 z+22032 z^2+59328 z^3+34704 z^4+3600 z^5
421	3211	48+1024 z+6910 z^2+17320 z^3+14524 z^4+2648 z^5	8+3824 z+52064 z^2+120064 z^3+60664 z^4+5296 z^5
421	31111	36+726 z+4554 z^2+10308 z^3+7356 z^4+960 z^5	24+4992 z+49920 z^2+90048 z^3+34536 z^4+1920 z^5
421	2221	36+712 z+4360 z^2+9568 z^3+6544 z^4+800 z^5	32+6080 z+53888 z^2+88576 z^3+31264 z^4+1600 z^5
421	22111	48+904 z+5176 z^2+10240 z^3+5728 z^4+320 z^5	128+11648 z+83648 z^2+114688 z^3+31168 z^4+640 z^5
421	211111	36+624 z+3192 z^2+5328 z^3+2160 z^4	288+14976 z+77184 z^2+76032 z^3+12960 z^4
421	1111111	12+174 z+678 z^2+672 z^3	432+10944 z+32976 z^2+16128 z^3
4111	4111	24+594 z+4812 z^2+15306 z^3+18090 z^4+6084 z^5+252 z^6	8748 z^2+49824 z^3+51480 z^4+10656 z^5+252 z^6
4111	3211	48+1044 z+7212 z^2+18624 z^3+16272 z^4+3168 z^5	2880 z+46944 z^2+119808 z^3+65952 z^4+6336 z^5
4111	31111	72+1548 z+10548 z^2+26784 z^3+22896 z^4+4320 z^5	5184 z+75168 z^2+179712 z^3+94176 z^4+8640 z^5
4111	2221	24+450 z+2544 z^2+4866 z^3+2430 z^4	36+5472 z+42408 z^2+58464 z^3+14580 z^4
4111	22111	72+1404 z+8460 z^2+18216 z^3+12168 z^4+1440 z^5	144+14400 z+112896 z^2+173952 z^3+58608 z^4+2880 z^5
4111	211111	72+1314 z+7200 z^2+13266 z^3+6318 z^4	324+21600 z+136296 z^2+166752 z^3+37908 z^4
4111	1111111	24+360 z+1464 z^2+1536 z^3	576+18432 z+65088 z^2+36864 z^3
331	331	24+580 z+4588 z^2+14264 z^3+16536 z^4+5520 z^5+240 z^6	384 z+12048 z^2+51072 z^3+47616 z^4+9600 z^5+240 z^6
331	322	24+532 z+3764 z^2+10032 z^3+9168 z^4+1920 z^5	1152 z+21024 z^2+59136 z^3+35808 z^4+3840 z^5
331	3211	48+1040 z+7164 z^2+18484 z^3+16204 z^4+3200 z^5	8+3392 z+48176 z^2+118720 z^3+65224 z^4+6400 z^5
331	31111	24+460 z+2672 z^2+5292 z^3+2772 z^4	24+4416 z+39408 z^2+60480 z^3+16632 z^4
331	2221	48+968 z+6072 z^2+13744 z^3+9808 z^4+1280 z^5	32+6656 z+66560 z^2+120064 z^3+46048 z^4+2560 z^5
331	22111	72+1436 z+8940 z^2+20272 z^3+14896 z^4+2240 z^5	128+12800 z+104672 z^2+173824 z^3+66976 z^4+4480 z^5
331	211111	48+856 z+4552 z^2+8048 z^3+3600 z^4	288+16896 z+96384 z^2+106752 z^3+21600 z^4
331	1111111	24+396 z+1908 z^2+2952 z^3+1080 z^4	432+13824 z+55296 z^2+44928 z^3+6480 z^4
322	322	36+846 z+6470 z^2+19280 z^3+21120 z^4+6480 z^5+240 z^6	960 z+22560 z^2+80640 z^3+65520 z^4+11520 z^5+240 z^6
322	3211	36+774 z+5282 z^2+13468 z^3+11620 z^4+2240 z^5	8+2816 z+37664 z^2+89152 z^3+47320 z^4+4480 z^5
322	31111	36+738 z+4742 z^2+11156 z^3+8556 z^4+1344 z^5	24+4608 z+46944 z^2+89280 z^3+37896 z^4+2688 z^5
322	2221	72+1524 z+10208 z^2+25432 z^3+21280 z^4+3920 z^5	32+6944 z+81536 z^2+178048 z^3+88480 z^4+7840 z^5
322	22111	72+1416 z+8624 z^2+18832 z^3+12832 z^4+1568 z^5	128+13376 z+109568 z^2+175360 z^3+61312 z^4+3136 z^5
322	211111	72+1356 z+7824 z^2+15912 z^3+9792 z^4+1008 z^5	288+19296 z+125568 z^2+167040 z^3+48672 z^4+2016 z^5
322	1111111	36+618 z+3138 z^2+5232 z^3+2160 z^4	432+16704 z+77616 z^2+73728 z^3+12960 z^4
3211	3211	48+1072 z+7708 z^2+21244 z^3+20932 z^4+5456 z^5+144 z^6	8+2816 z+41984 z^2+113728 z^3+73192 z^4+10048 z^5+144 z^6
3211	31111	48+1008 z+6684 z^2+16428 z^3+13476 z^4+2400 z^5	24+4992 z+56400 z^2+118848 z^3+56856 z^4+4800 z^5
3211	2221	48+1000 z+6568 z^2+15952 z^3+12880 z^4+2240 z^5	32+5504 z+58496 z^2+118528 z^3+54880 z^4+4480 z^5
3211	22111	96+1948 z+12388 z^2+28864 z^3+22000 z^4+3488 z^5	128+14528 z+130592 z^2+234496 z^3+97120 z^4+6976 z^5
3211	211111	96+1848 z+10968 z^2+23184 z^3+15120 z^4+1728 z^5	288+21888 z+156672 z^2+228096 z^3+73440 z^4+3456 z^5
3211	1111111	48+840 z+4368 z^2+7512 z^3+3240 z^4	432+19584 z+99936 z^2+102528 z^3+19440 z^4
31111	31111	120+2688 z+19368 z^2+53400 z^3+52440 z^4+13488 z^5+336 z^6	6144 z+102480 z^2+286080 z^3+184800 z^4+24960 z^5+336 z^6
31111	22111	120+2448 z+15672 z^2+36840 z^3+28440 z^4+4608 z^5	144+17280 z+159840 z^2+293760 z^3+124560 z^4+9216 z^5
31111	211111	240+4848 z+30672 z^2+71040 z^3+53760 z^4+8448 z^5	384+38400 z+332160 z^2+583680 z^3+238080 z^4+16896 z^5
31111	1111111	120+2160 z+11640 z^2+21000 z^3+9720 z^4	720+40320 z+234720 z^2+270720 z^3+58320 z^4
2221	2221	144+3180 z+22554 z^2+61086 z^3+58770 z^4+14760 z^5+360 z^6	36+9792 z+134208 z^2+343584 z^3+210420 z^4+27360 z^5+360 z^6
2221	22111	144+2964 z+19188 z^2+45768 z^3+36072 z^4+6048 z^5	144+19008 z+184896 z^2+353664 z^3+155952 z^4+12096 z^5
2221	211111	144+2844 z+17478 z^2+38898 z^3+27702 z^4+3888 z^5	324+27648 z+216216 z^2+346464 z^3+127332 z^4+7776 z^5
2221	1111111	144+2760 z+16344 z^2+34656 z^3+23040 z^4+2880 z^5	576+35712 z+237888 z^2+336384 z^3+109440 z^4+5760 z^5
22111	22111	240+5148 z+35232 z^2+91140 z^3+82260 z^4+18648 z^5+360 z^6	144+23040 z+259560 z^2+578880 z^3+312480 z^4+35136 z^5+360 z^6
22111	211111	240+4848 z+30672 z^2+71040 z^3+53760 z^4+8448 z^5	384+38400 z+332160 z^2+583680 z^3+238080 z^4+16896 z^5
22111	1111111	240+4680 z+28320 z^2+61800 z^3+42840 z^4+5760 z^5	720+51840 z+375840 z^2+570240 z^3+199440 z^4+11520 z^5
211111	211111	720+15240 z+102600 z^2+259800 z^3+227520 z^4+49080 z^5+840 z^6	600+79680 z+828120 z^2+1739520 z^3+886920 z^4+93120 z^5+840 z^6
211111	1111111	720+14400 z+90000 z^2+205200 z^3+151920 z^4+23040 z^5	1440+126720 z+1033920 z^2+1739520 z^3+681120 z^4+46080 z^5
1111111	1111111	5040+105840 z+705600 z^2+1764000 z^3+1517040 z^4+317520 z^5+5040 z^6	5040+604800 z+6002640 z^2+12176640 z^3+6002640 z^4+604800 z^5+5040 z^6
8	8	1+56 z+1176 z^2+11760 z^3+58800 z^4+141120 z^5+141120 z^6+40320 z^7	40320 z^7
8	71	7+336 z+5880 z^2+47040 z^3+176400 z^4+282240 z^5+141120 z^6	282240 z^6
8	62	20+840 z+12600 z^2+84000 z^3+252000 z^4+302400 z^5+100800 z^6	604800 z^5+201600 z^6
8	611	21+840 z+11760 z^2+70560 z^3+176400 z^4+141120 z^5	846720 z^5
8	53	28+1064 z+14280 z^2+84000 z^3+218400 z^4+221760 z^5+60480 z^6	403200 z^4+604800 z^5+120960 z^6
8	521	64+2240 z+26880 z^2+134400 z^3+268800 z^4+161280 z^5	1612800 z^4+967680 z^5
8	5111	35+1120 z+11760 z^2+47040 z^3+58800 z^4	1411200 z^4
8	44	14+504 z+6384 z^2+35280 z^3+85680 z^4+80640 z^5+20160 z^6	40320 z^3+241920 z^4+241920 z^5+40320 z^6
8	431	70+2240 z+24360 z^2+109200 z^3+193200 z^4+100800 z^5	604800 z^3+1612800 z^4+604800 z^5
8	422	56+1680 z+16800 z^2+67200 z^3+100800 z^4+40320 z^5	806400 z^3+1209600 z^4+241920 z^5
8	4211	90+2520 z+22680 z^2+75600 z^3+75600 z^4	1814400 z^3+1814400 z^4
8	41111	35+840 z+5880 z^2+11760 z^3	1411200 z^3
8	332	42+1176 z+10920 z^2+40320 z^3+55440 z^4+20160 z^5	120960 z^2+725760 z^3+725760 z^4+120960 z^5
8	3311	56+1456 z+12096 z^2+36960 z^3+33600 z^4	241920 z^2+1209600 z^3+806400 z^4
8	3221	70+1680 z+12600 z^2+33600 z^3+25200 z^4	604800 z^2+1612800 z^3+604800 z^4
8	32111	64+1344 z+8064 z^2+13440 z^3	967680 z^2+1612800 z^3
8	311111	21+336 z+1176 z^2	846720 z^2
8	2222	14+280 z+1680 z^2+3360 z^3+1680 z^4	40320 z+241920 z^2+241920 z^3+40320 z^4
8	22211	28+504 z+2520 z^2+3360 z^3	120960 z+604800 z^2+403200 z^3
8	221111	20+280 z+840 z^2	201600 z+604800 z^2
8	2111111	7+56 z	282240 z
8	11111111	1	40320
71	71	2+92 z+1548 z^2+12000 z^3+44400 z^4+73440 z^5+44640 z^6+5760 z^7	25920 z^5+48960 z^6+5760 z^7
71	62	10+400 z+5700 z^2+36000 z^3+102000 z^4+115200 z^5+36000 z^6	72000 z^4+259200 z^5+72000 z^6
71	611	12+474 z+6660 z^2+41400 z^3+115200 z^4+127440 z^5+38880 z^6	108000 z^4+298080 z^5+77760 z^6
71	53	18+648 z+8172 z^2+44640 z^3+105840 z^4+95040 z^5+21600 z^6	34560 z^3+336960 z^4+311040 z^5+43200 z^6
71	521	48+1656 z+19800 z^2+100800 z^3+216000 z^4+164160 z^5+25920 z^6	172800 z^3+1036800 z^4+673920 z^5+51840 z^6
71	5111	30+990 z+11160 z^2+52200 z^3+97200 z^4+54000 z^5	172800 z^3+712800 z^4+324000 z^5
71	44	10+340 z+4020 z^2+20400 z^3+44400 z^4+36000 z^5+7200 z^6	57600 z^3+201600 z^4+129600 z^5+14400 z^6
71	431	60+1890 z+20340 z^2+91440 z^3+168480 z^4+105840 z^5+12960 z^6	25920 z^2+630720 z^3+1257120 z^4+479520 z^5+25920 z^6
71	422	52+1564 z+15840 z^2+65280 z^3+104160 z^4+47520 z^5	51840 z^2+685440 z^3+1074240 z^4+285120 z^5
71	4211	90+2610 z+25200 z^2+97200 z^3+140400 z^4+54000 z^5	129600 z^2+1425600 z^3+1749600 z^4+324000 z^5
71	41111	40+1060 z+9000 z^2+28200 z^3+26400 z^4	129600 z^2+849600 z^3+633600 z^4
71	332	42+1182 z+11088 z^2+41760 z^3+59760 z^4+23760 z^5	129600 z^2+699840 z^3+721440 z^4+142560 z^5
71	3311	60+1620 z+14400 z^2+50400 z^3+64800 z^4+21600 z^5	259200 z^2+1123200 z^3+907200 z^4+129600 z^5
71	3221	80+2030 z+16620 z^2+51600 z^3+54000 z^4+10800 z^5	14400 z+518400 z^2+1656000 z^3+972000 z^4+64800 z^5
71	32111	80+1880 z+13800 z^2+36000 z^3+26400 z^4	28800 z+777600 z^2+1785600 z^3+633600 z^4
71	311111	30+600 z+3420 z^2+5400 z^3	43200 z+518400 z^2+648000 z^3
71	2222	18+396 z+2700 z^2+6480 z^3+4320 z^4	25920 z+233280 z^2+362880 z^3+103680 z^4
71	22211	38+788 z+4932 z^2+10320 z^3+5280 z^4	77760 z+596160 z^2+731520 z^3+126720 z^4
71	221111	30+540 z+2700 z^2+3600 z^3	129600 z+648000 z^2+432000 z^3
71	2111111	12+162 z+468 z^2	4320+142560 z+336960 z^2
71	11111111	2+14 z	10080+70560 z
62	62	4+158 z+2244 z^2+14364 z^3+42624 z^4+54288 z^5+23904 z^6+2016 z^7	3456 z^3+40896 z^4+81216 z^5+33696 z^6+2016 z^7
62	611	4+150 z+1992 z^2+11640 z^3+30240 z^4+30960 z^5+8640 z^6	5760 z^3+56160 z^4+82080 z^5+17280 z^6
62	53	12+426 z+5316 z^2+28908 z^3+68976 z^4+63648 z^5+15552 z^6	864 z^2+44064 z^3+212544 z^4+195264 z^5+31104 z^6
62	521	32+1088 z+12896 z^2+65824 z^3+144768 z^4+119424 z^5+24576 z^6	6912 z^2+183552 z^3+628992 z^4+421632 z^5+49152 z^6
62	5111	20+650 z+7280 z^2+34480 z^3+68160 z^4+47280 z^5+6720 z^6	8640 z^2+162240 z^3+419040 z^4+203040 z^5+13440 z^6
62	44	8+268 z+3120 z^2+15576 z^3+33312 z^4+26496 z^5+5184 z^6	1728 z^2+53568 z^3+160128 z^4+96768 z^5+10368 z^6
62	431	52+1630 z+17512 z^2+78992 z^3+147264 z^4+94992 z^5+12288 z^6	46656 z^2+549696 z^3+1053216 z^4+422496 z^5+24576 z^6
62	422	48+1464 z+15276 z^2+66912 z^3+121872 z^4+79200 z^5+12096 z^6	576 z+70848 z^2+597888 z^3+911808 z^4+330048 z^5+24192 z^6
62	4211	84+2466 z+24420 z^2+98952 z^3+157968 z^4+77616 z^5+4032 z^6	1728 z+171072 z^2+1204992 z^3+1583712 z^4+417312 z^5+8064 z^6
62	41111	40+1100 z+10020 z^2+36240 z^3+48720 z^4+17280 z^5	2880 z+146880 z^2+708480 z^3+650880 z^4+103680 z^5
62	332	44+1266 z+12300 z^2+49152 z^3+78768 z^4+41616 z^5+4032 z^6	1728 z+127872 z^2+672192 z^3+762912 z^4+201312 z^5+8064 z^6
62	3311	64+1768 z+16252 z^2+59888 z^3+84048 z^4+34080 z^5+1344 z^6	5184 z+240192 z^2+1108992 z^3+1035072 z^4+188352 z^5+2688 z^6
62	3221	92+2446 z+21504 z^2+75096 z^3+98208 z^4+34992 z^5	18432 z+490752 z^2+1683072 z^3+1307232 z^4+209952 z^5
62	32111	96+2400 z+19392 z^2+59712 z^3+62976 z^4+13824 z^5	36864 z+705024 z^2+1949184 z^3+1096704 z^4+82944 z^5
62	311111	40+900 z+6300 z^2+15600 z^3+10800 z^4	43200 z+475200 z^2+835200 z^3+259200 z^4
62	2222	24+576 z+4464 z^2+13248 z^3+13824 z^4+3456 z^5	20736 z+228096 z^2+470016 z^3+228096 z^4+20736 z^5
62	22211	52+1190 z+8604 z^2+22764 z^3+18672 z^4+1728 z^5	62208 z+584928 z^2+1042848 z^3+396288 z^4+10368 z^5
62	221111	44+914 z+5756 z^2+12220 z^3+6480 z^4	960+95040 z+678240 z^2+844320 z^3+155520 z^4
62	2111111	20+350 z+1700 z^2+2200 z^3	2400+108000 z+432000 z^2+264000 z^3
62	11111111	4+50 z+132 z^2	4320+61920 z+95040 z^2
611	611	6+238 z+3376 z^2+21400 z^3+62000 z^4+75120 z^5+29760 z^6+1920 z^7	60000 z^4+133920 z^5+46080 z^6+1920 z^7
611	521	24+832 z+10064 z^2+52480 z^3+118080 z^4+99840 z^5+21120 z^6	107520 z^3+472320 z^4+345600 z^5+42240 z^6
611	5111	30+1030 z+12320 z^2+63400 z^3+140400 z^4+116400 z^5+24000 z^6	153600 z^3+597600 z^4+410400 z^5+48000 z^6
611	431	30+950 z+10360 z^2+47840 z^3+92880 z^4+65040 z^5+10560 z^6	25920 z^2+304320 z^3+594720 z^4+263520 z^5+21120 z^6
611	422	36+1068 z+10656 z^2+43200 z^3+67680 z^4+30240 z^5	51840 z^2+501120 z^3+717120 z^4+181440 z^5
611	4211	90+2730 z+28200 z^2+121200 z^3+212400 z^4+126000 z^5+14400 z^6	129600 z^2+1137600 z^3+1749600 z^4+583200 z^5+28800 z^6
611	41111	60+1740 z+16920 z^2+66600 z^3+100800 z^4+43200 z^5	129600 z^2+907200 z^3+1123200 z^4+259200 z^5
611	332	30+830 z+7640 z^2+28160 z^3+39280 z^4+15120 z^5	1920 z+112320 z^2+515520 z^3+489120 z^4+90720 z^5
611	3311	60+1700 z+16240 z^2+63680 z^3+99840 z^4+51360 z^5+4800 z^6	5760 z+207360 z^2+946560 z^3+999360 z^4+250560 z^5+9600 z^6
611	3221	90+2370 z+20520 z^2+69840 z^3+87120 z^4+28080 z^5	17280 z+492480 z^2+1702080 z^3+1248480 z^4+168480 z^5
611	32111	120+3120 z+26640 z^2+89280 z^3+109440 z^4+34560 z^5	34560 z+725760 z^2+2280960 z^3+1589760 z^4+207360 z^5
611	311111	60+1420 z+10600 z^2+28600 z^3+22400 z^4	38400 z+561600 z^2+1281600 z^3+537600 z^4
611	2222	24+552 z+3984 z^2+10320 z^3+7680 z^4	23040 z+259200 z^2+501120 z^3+184320 z^4
611	22211	60+1380 z+10080 z^2+27360 z^3+24480 z^4+4320 z^5	69120 z+673920 z^2+1192320 z^3+457920 z^4+25920 z^5
611	221111	60+1300 z+8720 z^2+20560 z^3+13440 z^4	960+106560 z+812160 z^2+1176960 z^3+322560 z^4
611	2111111	30+550 z+2840 z^2+4000 z^3	2400+122400 z+604800 z^2+480000 z^3
611	11111111	6+78 z+216 z^2	4320+82080 z+155520 z^2
53	53	8+292 z+3792 z^2+21888 z^3+57456 z^4+62928 z^5+22752 z^6+1440 z^7	864 z^2+26784 z^3+123264 z^4+134784 z^5+35424 z^6+1440 z^7
53	521	16+536 z+6264 z^2+31584 z^3+68928 z^4+57024 z^5+12096 z^6	6912 z^2+110592 z^3+306432 z^4+196992 z^5+24192 z^6
53	5111	8+244 z+2520 z^2+10680 z^3+17760 z^4+8640 z^5	8640 z^2+95040 z^3+167040 z^4+51840 z^5
53	44	8+276 z+3336 z^2+17496 z^3+40032 z^4+35136 z^5+8064 z^6	1728 z^2+42048 z^3+148608 z^4+114048 z^5+16128 z^6
53	431	48+1536 z+17004 z^2+80256 z^3+161016 z^4+118800 z^5+21168 z^6	288 z+44064 z^2+454464 z^3+935424 z^4+458784 z^5+42336 z^6
53	422	40+1212 z+12540 z^2+54216 z^3+96264 z^4+58608 z^5+7056 z^6	864 z+68256 z^2+498816 z^3+763776 z^4+266976 z^5+14112 z^6
53	4211	72+2124 z+21276 z^2+88344 z^3+148824 z^4+84240 z^5+9072 z^6	2592 z+163296 z^2+1005696 z^3+1316736 z^4+396576 z^5+18144 z^6
53	41111	32+864 z+7704 z^2+27168 z^3+35424 z^4+12096 z^5	3456 z+141696 z^2+585216 z^3+487296 z^4+72576 z^5
53	332	48+1416 z+14244 z^2+59904 z^3+104184 z^4+64080 z^5+9072 z^6	2592 z+120096 z^2+668736 z^3+850176 z^4+275616 z^5+18144 z^6
53	3311	72+2052 z+19692 z^2+77208 z^3+119208 z^4+56880 z^5+3024 z^6	6624 z+227232 z^2+1112832 z^3+1245312 z^4+304992 z^5+6048 z^6
53	3221	104+2844 z+26028 z^2+96696 z^3+141048 z^4+65232 z^5+5040 z^6	19872 z+477792 z^2+1775232 z^3+1579392 z^4+330912 z^5+10080 z^6
53	32111	112+2904 z+24744 z^2+82848 z^3+101664 z^4+32256 z^5	38016 z+694656 z^2+2117376 z^3+1472256 z^4+193536 z^5
53	311111	48+1128 z+8448 z^2+23616 z^3+21888 z^4+4032 z^5	41472 z+490752 z^2+974592 z^3+404352 z^4+24192 z^5
53	2222	32+808 z+6696 z^2+21792 z^3+26016 z^4+8064 z^5	19584 z+238464 z^2+601344 z^3+382464 z^4+48384 z^5
53	22211	72+1764 z+14076 z^2+43644 z^3+48960 z^4+14112 z^5	288+56160 z+626400 z^2+1383840 z^3+751680 z^4+84672 z^5
53	221111	64+1448 z+10332 z^2+26892 z^3+21600 z^4+2016 z^5	864+87840 z+747360 z^2+1274400 z^3+457920 z^4+12096 z^5
53	2111111	32+640 z+3864 z^2+7848 z^3+4032 z^4	1728+99648 z+537408 z^2+554688 z^3+96768 z^4
53	11111111	8+132 z+600 z^2+720 z^3	2880+60480 z+172800 z^2+86400 z^3
521	521	12+412 z+4973 z^2+26230 z^3+61305 z^4+57225 z^5+16170 z^6+630 z^7	4050 z^2+71070 z^3+217620 z^4+162540 z^5+27930 z^6+630 z^7
521	5111	12+394 z+4490 z^2+21910 z^3+45720 z^4+35400 z^5+6720 z^6	6480 z^2+95280 z^3+236880 z^4+131760 z^5+13440 z^6
521	431	24+752 z+8122 z^2+37214 z^3+71952 z^4+50568 z^5+8400 z^6	288 z+29808 z^2+256368 z^3+461808 z^4+202608 z^5+16800 z^6
521	422	36+1110 z+11772 z^2+52812 z^3+99576 z^4+67824 z^5+10800 z^6	864 z+57024 z^2+415584 z^3+679104 z^4+277344 z^5+21600 z^6
521	4211	72+2172 z+22422 z^2+97170 z^3+174816 z^4+111096 z^5+15696 z^6	2592 z+141264 z^2+915984 z^3+1333584 z^4+478224 z^5+31392 z^6
521	41111	48+1392 z+13680 z^2+55584 z^3+91296 z^4+50112 z^5+5184 z^6	3456 z+134784 z^2+705024 z^3+843264 z^4+238464 z^5+10368 z^6
521	332	36+1038 z+10128 z^2+40776 z^3+66168 z^4+35712 z^5+3600 z^6	2592 z+106272 z^2+539712 z^3+624672 z^4+171072 z^5+7200 z^6
521	3311	60+1706 z+16384 z^2+64760 z^3+102792 z^4+53952 z^5+5232 z^6	6624 z+204768 z^2+931008 z^3+1005408 z^4+260928 z^5+10464 z^6
521	3221	108+2982 z+27648 z^2+104616 z^3+156888 z^4+76032 z^5+6480 z^6	19872 z+469152 z^2+1795392 z^3+1678752 z^4+378432 z^5+12960 z^6
521	32111	132+3528 z+31365 z^2+111960 z^3+153261 z^4+62019 z^5+2592 z^6	54+37530 z+703404 z^2+2339604 z^3+1895454 z^4+341010 z^5+5184 z^6
521	311111	72+1812 z+14916 z^2+47940 z^3+55944 z^4+16632 z^5	144+40176 z+539136 z^2+1380096 z^3+843696 z^4+99792 z^5
521	2222	36+918 z+7710 z^2+25602 z^3+31656 z^4+10584 z^5	19584 z+257904 z^2+668304 z^3+442224 z^4+63504 z^5
521	22211	84+2082 z+16830 z^2+52902 z^3+60012 z^4+17172 z^5	216+56808 z+684288 z^2+1617408 z^3+925128 z^4+103032 z^5
521	221111	84+1978 z+14942 z^2+42622 z^3+41220 z^4+8316 z^5	744+88920 z+851040 z^2+1656480 z^3+739800 z^4+49896 z^5
521	2111111	48+1024 z+6752 z^2+15616 z^3+9984 z^4	1536+101376 z+677376 z^2+915456 z^3+239616 z^4
521	11111111	12+210 z+1026 z^2+1350 z^3	2160+66960 z+252720 z^2+162000 z^3
5111	5111	24+840 z+10320 z^2+55248 z^3+130368 z^4+121536 z^5+33408 z^6+1152 z^7	110592 z^3+444672 z^4+352512 z^5+58752 z^6+1152 z^7
5111	4211	72+2232 z+23760 z^2+106704 z^3+200448 z^4+134784 z^5+20736 z^6	93312 z^2+819072 z^3+1389312 z^4+559872 z^5+41472 z^6
5111	41111	96+2952 z+31128 z^2+138216 z^3+256032 z^4+169056 z^5+25344 z^6	139968 z^2+1136448 z^3+1833408 z^4+710208 z^5+50688 z^6
5111	3311	48+1392 z+13728 z^2+56352 z^3+94848 z^4+55296 z^5+6912 z^6	4608 z+145152 z^2+698112 z^3+824832 z^4+248832 z^5+13824 z^6
5111	3221	72+1944 z+17424 z^2+62352 z^3+84096 z^4+31104 z^5	13824 z+342144 z^2+1275264 z^3+1085184 z^4+186624 z^5
5111	32111	192+5328 z+49728 z^2+189888 z^3+288576 z^4+142848 z^5+12672 z^6	34560 z+808704 z^2+3147264 z^3+3020544 z^4+705024 z^5+25344 z^6
5111	311111	144+3816 z+33480 z^2+116856 z^3+152928 z^4+54432 z^5	41472 z+793152 z^2+2607552 z^3+2037312 z^4+326592 z^5
5111	2222	24+552 z+3984 z^2+10320 z^3+7680 z^4	23040 z+259200 z^2+501120 z^3+184320 z^4
5111	22211	96+2376 z+19176 z^2+60168 z^3+68112 z^4+19440 z^5	288+66528 z+787968 z^2+1847808 z^3+1051488 z^4+116640 z^5
5111	221111	144+3528 z+28152 z^2+87192 z^3+97200 z^4+27216 z^5	864+116640 z+1244160 z^2+2764800 z^3+1516320 z^4+163296 z^5
5111	2111111	96+2136 z+14856 z^2+36888 z^3+26112 z^4	1728+145728 z+1176768 z^2+1919808 z^3+626688 z^4
5111	11111111	24+432 z+2184 z^2+3000 z^3	2880+112320 z+492480 z^2+360000 z^3
44	44	16+592 z+7788 z^2+45480 z^3+120480 z^4+132480 z^5+47520 z^6+2880 z^7	40320 z^3+241920 z^4+285120 z^5+74880 z^6+2880 z^7
44	431	48+1584 z+18180 z^2+89640 z^3+190080 z^4+151200 z^5+30240 z^6	25920 z^2+371520 z^3+933120 z^4+544320 z^5+60480 z^6
44	422	32+992 z+10584 z^2+47808 z^3+90864 z^4+62496 z^5+10080 z^6	576 z+46656 z^2+360576 z^3+608256 z^4+254016 z^5+20160 z^6
44	4211	48+1392 z+13572 z^2+53784 z^3+82512 z^4+36288 z^5	1728 z+114048 z^2+710208 z^3+891648 z^4+217728 z^5
44	41111	16+400 z+3180 z^2+9240 z^3+7920 z^4	2880 z+103680 z^2+348480 z^3+190080 z^4
44	332	48+1392 z+13572 z^2+53784 z^3+82512 z^4+36288 z^5	1728 z+114048 z^2+710208 z^3+891648 z^4+217728 z^5
44	3311	96+2880 z+29592 z^2+127872 z^3+230256 z^4+147744 z^5+21600 z^6	5184 z+212544 z^2+1240704 z^3+1741824 z^4+627264 z^5+43200 z^6
44	3221	112+3088 z+28548 z^2+107496 z^3+160128 z^4+77472 z^5+7200 z^6	18432 z+482112 z^2+1887552 z^3+1734912 z^4+378432 z^5+14400 z^6
44	32111	128+3392 z+29760 z^2+103872 z^3+135936 z^4+48384 z^5	36864 z+705024 z^2+2317824 z^3+1810944 z^4+290304 z^5
44	311111	48+1104 z+7956 z^2+20520 z^3+15120 z^4	43200 z+518400 z^2+1010880 z^3+362880 z^4
44	2222	48+1296 z+11844 z^2+44928 z^3+69984 z^4+38016 z^5+4320 z^6	20736 z+279936 z^2+781056 z^3+668736 z^4+176256 z^5+8640 z^6
44	22211	96+2400 z+19608 z^2+62472 z^3+72144 z^4+21168 z^5	288+59616 z+746496 z^2+1840896 z^3+1096416 z^4+127008 z^5
44	221111	96+2304 z+17928 z^2+53784 z^3+57456 z^4+15120 z^5	864+95904 z+912384 z^2+1845504 z^3+925344 z^4+90720 z^5
44	2111111	48+1008 z+6516 z^2+14688 z^3+9072 z^4	1728+114048 z+710208 z^2+891648 z^3+217728 z^4
44	11111111	16+304 z+1740 z^2+3360 z^3+1680 z^4	2880+74880 z+285120 z^2+241920 z^3+40320 z^4
431	431	24+780 z+8844 z^2+43368 z^3+92856 z^4+77616 z^5+18864 z^6+576 z^7	288 z+23328 z^2+212544 z^3+445824 z^4+251424 z^5+33696 z^6+576 z^7
431	422	24+732 z+7668 z^2+33912 z^3+62856 z^4+41904 z^5+6480 z^6	864 z+44064 z^2+290304 z^3+445824 z^4+173664 z^5+12960 z^6
431	4211	48+1440 z+14796 z^2+63936 z^3+115128 z^4+73872 z^5+10800 z^6	2592 z+106272 z^2+620352 z^3+870912 z^4+313632 z^5+21600 z^6
431	41111	24+660 z+6048 z^2+22248 z^3+31104 z^4+12096 z^5	3456 z+98496 z^2+409536 z^3+383616 z^4+72576 z^5
431	332	48+1440 z+14796 z^2+63936 z^3+115128 z^4+73872 z^5+10800 z^6	2592 z+106272 z^2+620352 z^3+870912 z^4+313632 z^5+21600 z^6
431	3311	72+2116 z+21236 z^2+89272 z^3+155496 z^4+95664 z^5+13200 z^6	6624 z+199584 z^2+996864 z^3+1257984 z^4+415584 z^5+26400 z^6
431	3221	120+3364 z+31800 z^2+123452 z^3+191872 z^4+98152 z^5+9200 z^6	16+19728 z+469728 z^2+1915648 z^3+1936368 z^4+478512 z^5+18400 z^6
431	32111	144+3928 z+35952 z^2+134192 z^3+198400 z^4+94816 z^5+8000 z^6	64+37440 z+696960 z^2+2425600 z^3+2157120 z^4+472896 z^5+16000 z^6
431	311111	72+1812 z+14916 z^2+47940 z^3+55944 z^4+16632 z^5	144+40176 z+539136 z^2+1380096 z^3+843696 z^4+99792 z^5
431	2222	48+1264 z+11084 z^2+39220 z^3+54168 z^4+23784 z^5+1920 z^6	48+19152 z+292032 z^2+856512 z^3+644112 z^4+119664 z^5+3840 z^6
431	22211	120+3124 z+27000 z^2+93632 z^3+125152 z^4+51232 z^5+3200 z^6	256+56448 z+776448 z^2+2167168 z^3+1562688 z^4+268992 z^5+6400 z^6
431	221111	120+2980 z+24224 z^2+77080 z^3+89712 z^4+27216 z^5	672+89568 z+978048 z^2+2270208 z^3+1336608 z^4+163296 z^5
431	2111111	72+1644 z+11964 z^2+32556 z^3+29544 z^4+5400 z^5	1296+103536 z+824256 z^2+1394496 z^3+547056 z^4+32400 z^5
431	11111111	24+492 z+3096 z^2+6768 z^3+4032 z^4	1728+70848 z+373248 z^2+425088 z^3+96768 z^4
422	422	36+1158 z+12972 z^2+62688 z^3+131784 z^4+107496 z^5+25200 z^6+720 z^7	576 z+40176 z^2+338256 z^3+668736 z^4+357696 z^5+45360 z^6+720 z^7
422	4211	36+1086 z+11232 z^2+48924 z^3+88992 z^4+57888 z^5+8640 z^6	1728 z+75168 z^2+455328 z^3+658368 z^4+243648 z^5+17280 z^6
422	41111	36+1050 z+10416 z^2+42996 z^3+72672 z^4+42336 z^5+5184 z^6	2880 z+101088 z^2+515808 z^3+629568 z^4+191808 z^5+10368 z^6
422	332	36+1086 z+11232 z^2+48924 z^3+88992 z^4+57888 z^5+8640 z^6	1728 z+75168 z^2+455328 z^3+658368 z^4+243648 z^5+17280 z^6
422	3311	36+1014 z+9636 z^2+37632 z^3+58896 z^4+30384 z^5+2880 z^6	5184 z+134784 z^2+569664 z^3+588384 z^4+147744 z^5+5760 z^6
422	3221	144+4152 z+40720 z^2+166312 z^3+278872 z^4+162472 z^5+20480 z^6	16+18288 z+469728 z^2+2114848 z^3+2433168 z^4+729072 z^5+40960 z^6
422	32111	144+3936 z+36112 z^2+135184 z^3+200608 z^4+96352 z^5+8192 z^6	64+36288 z+686592 z^2+2417152 z^3+2169792 z^4+479808 z^5+16384 z^6
422	311111	108+2862 z+25296 z^2+90372 z^3+126072 z^4+55368 z^5+4032 z^6	144+41904 z+632448 z^2+1902528 z^3+1485648 z^4+283824 z^5+8064 z^6
422	2222	72+1980 z+18384 z^2+70416 z^3+109416 z^4+58296 z^5+6720 z^6	48+20304 z+346464 z^2+1174944 z^3+1078704 z^4+269136 z^5+13440 z^6
422	22211	144+3780 z+32944 z^2+115000 z^3+153376 z^4+59968 z^5+2240 z^6	256+59904 z+874944 z^2+2584384 z^3+1949184 z^4+332928 z^5+4480 z^6
422	221111	144+3612 z+29760 z^2+96648 z^3+116880 z^4+39696 z^5+1344 z^6	672+97632 z+1123200 z^2+2705280 z^3+1654560 z^4+222048 z^5+2688 z^6
422	2111111	108+2574 z+19872 z^2+59076 z^3+62424 z^4+16200 z^5	1296+117936 z+1057536 z^2+2068416 z^3+1012176 z^4+97200 z^5
422	11111111	36+762 z+4992 z^2+11508 z^3+7392 z^4	1728+85248 z+515808 z^2+671328 z^3+177408 z^4
4211	4211	48+1492 z+16040 z^2+73656 z^3+144880 z^4+107648 z^5+21728 z^6+448 z^7	1600 z+78912 z^2+535680 z^3+883840 z^4+394560 z^5+40320 z^6+448 z^7
4211	41111	48+1428 z+14520 z^2+61896 z^3+109392 z^4+68256 z^5+9504 z^6	2880 z+114048 z^2+641088 z^3+862848 z^4+295488 z^5+19008 z^6
4211	3311	48+1396 z+13824 z^2+57088 z^3+96976 z^4+57408 z^5+7392 z^6	4800 z+143424 z^2+689664 z^3+826944 z^4+255744 z^5+14784 z^6
4211	3221	96+2744 z+26636 z^2+107436 z^3+177304 z^4+101080 z^5+12320 z^6	16+14256 z+337536 z^2+1443136 z^3+1592496 z^4+458640 z^5+24640 z^6
4211	32111	192+5384 z+51056 z^2+199920 z^3+317056 z^4+170464 z^5+18752 z^6	64+37440 z+779904 z^2+3030784 z^3+3057984 z^4+797760 z^5+37504 z^6
4211	311111	144+3888 z+35172 z^2+129492 z^3+188280 z^4+88056 z^5+7200 z^6	144+45360 z+751680 z^2+2459520 z^3+2093040 z^4+441936 z^5+14400 z^6
4211	2222	48+1252 z+10788 z^2+36868 z^3+47032 z^4+16200 z^5	48+18768 z+295488 z^2+881088 z^3+642768 z^4+97200 z^5
4211	22211	144+3812 z+33680 z^2+120432 z^3+168592 z^4+74752 z^5+5600 z^6	256+59328 z+854208 z^2+2528128 z^3+1971648 z^4+381312 z^5+11200 z^6
4211	221111	192+4924 z+41736 z^2+140776 z^3+179680 z^4+66288 z^5+2400 z^6	672+107040 z+1339200 z^2+3525120 z^3+2395680 z^4+368928 z^5+4800 z^6
4211	2111111	144+3492 z+27540 z^2+84132 z^3+92232 z^4+25272 z^5	1296+133488 z+1306368 z^2+2757888 z^3+1455408 z^4+151632 z^5
4211	11111111	48+1032 z+6888 z^2+16248 z^3+10752 z^4	1728+99648 z+658368 z^2+917568 z^3+258048 z^4
41111	41111	120+3792 z+41448 z^2+193464 z^3+386400 z^4+290592 z^5+58752 z^6+1152 z^7	139968 z^2+1247040 z^3+2278080 z^4+1062720 z^5+109440 z^6+1152 z^7
41111	32111	240+6864 z+66624 z^2+268416 z^3+441600 z^4+249984 z^5+29952 z^6	32256 z+829440 z^2+3617280 z^3+3997440 z^4+1140480 z^5+59904 z^6
41111	311111	360+10224 z+98424 z^2+392616 z^3+637920 z^4+355104 z^5+41472 z^6	55296 z+1321920 z^2+5520960 z^3+5901120 z^4+1632960 z^5+82944 z^6
41111	22211	120+3072 z+25896 z^2+86184 z^3+106320 z^4+34992 z^5	288+61920 z+829440 z^2+2234880 z^3+1501920 z^4+209952 z^5
41111	221111	360+9504 z+83736 z^2+298584 z^3+416880 z^4+184464 z^5+13824 z^6	864+158112 z+2177280 z^2+6324480 z^3+4885920 z^4+940896 z^5+27648 z^6
41111	2111111	360+9072 z+75096 z^2+244584 z^3+293760 z^4+93312 z^5	1728+233280 z+2721600 z^2+6747840 z^3+4250880 z^4+559872 z^5
41111	11111111	120+2640 z+18120 z^2+44280 z^3+30720 z^4	2880+204480 z+1529280 z^2+2364480 z^3+737280 z^4
332	332	72+2268 z+24784 z^2+116200 z^3+235040 z^4+181920 z^5+39360 z^6+960 z^7	1920 z+103680 z^2+754560 z^3+1330560 z^4+639360 z^5+72000 z^6+960 z^7
332	3311	72+2124 z+21400 z^2+90320 z^3+157920 z^4+97440 z^5+13440 z^6	5760 z+190080 z^2+986880 z^3+1270080 z^4+423360 z^5+26880 z^6
332	3221	144+4176 z+41252 z^2+170076 z^3+288904 z^4+171640 z^5+22400 z^6	16+17136 z+449856 z^2+2076736 z^3+2456496 z^4+761040 z^5+44800 z^6
332	32111	144+3960 z+36608 z^2+138384 z^3+208096 z^4+101920 z^5+8960 z^6	64+33984 z+658944 z^2+2385664 z^3+2205504 z^4+504000 z^5+17920 z^6
332	311111	72+1836 z+15388 z^2+50764 z^3+61736 z^4+19800 z^5	144+37104 z+506304 z^2+1353024 z^3+887664 z^4+118800 z^5
332	2222	72+1908 z+16756 z^2+58628 z^3+77112 z^4+27720 z^5	48+22608 z+399168 z^2+1295808 z^3+1019088 z^4+166320 z^5
332	22211	216+5892 z+54104 z^2+203856 z^3+308224 z^4+155680 z^5+15680 z^6	256+66816 z+1080576 z^2+3586816 z^3+3197376 z^4+745920 z^5+31360 z^6
332	221111	216+5628 z+48784 z^2+170312 z^3+230928 z^4+97680 z^5+6720 z^6	672+109152 z+1406592 z^2+3860352 z^3+2813472 z^4+505440 z^5+13440 z^6
332	2111111	144+3504 z+27780 z^2+85596 z^3+95304 z^4+27000 z^5	1296+132336 z+1290816 z^2+2742336 z^3+1477296 z^4+162000 z^5
332	11111111	72+1668 z+12456 z^2+35568 z^3+35712 z^4+8640 z^5	1728+105408 z+787968 z^2+1358208 z^3+597888 z^4+51840 z^5
3311	3311	96+2944 z+31160 z^2+140464 z^3+270072 z^4+194808 z^5+37680 z^6+720 z^7	4608 z+185328 z^2+1135248 z^3+1742688 z^4+731808 z^5+70320 z^6+720 z^7
3311	3221	96+2752 z+26808 z^2+108608 z^3+180280 z^4+103624 z^5+12800 z^6	16+13680 z+329760 z^2+1431520 z^3+1602000 z^4+468144 z^5+25600 z^6
3311	32111	192+5440 z+52272 z^2+208304 z^3+338656 z^4+189280 z^5+22400 z^6	64+33984 z+728064 z^2+2946304 z^3+3121344 z^4+866880 z^5+44800 z^6
3311	311111	96+2496 z+21432 z^2+72960 z^3+92664 z^4+31752 z^5	144+40176 z+603936 z^2+1764576 z^3+1271376 z^4+190512 z^5
3311	2222	96+2656 z+24776 z^2+95008 z^3+146472 z^4+75480 z^5+7680 z^6	48+22608 z+429408 z^2+1561248 z^3+1481328 z^4+360720 z^5+15360 z^6
3311	22211	192+5152 z+46272 z^2+168896 z^3+242944 z^4+112000 z^5+8960 z^6	256+66816 z+1046016 z^2+3306496 z^3+2739456 z^4+564480 z^5+17920 z^6
3311	221111	288+7696 z+68960 z^2+252112 z^3+366576 z^4+175248 z^5+16128 z^6	672+118368 z+1646784 z^2+4931904 z^3+4024224 z^4+857952 z^5+32256 z^6
3311	2111111	192+4752 z+38472 z^2+121776 z^3+140664 z^4+42120 z^5	1296+149616 z+1588896 z^2+3636576 z^3+2112336 z^4+252720 z^5
3311	11111111	96+2256 z+17136 z^2+49968 z^3+51552 z^4+12960 z^5	1728+122688 z+995328 z^2+1824768 z^3+848448 z^4+77760 z^5
3221	3221	144+4272 z+43492 z^2+187060 z^3+338968 z^4+225688 z^5+38624 z^6+576 z^7	16+14256 z+389376 z^2+1922752 z^3+2503152 z^4+902736 z^5+73216 z^6+576 z^7
3221	32111	144+4056 z+38704 z^2+152944 z^3+246016 z^4+135520 z^5+15680 z^6	64+28224 z+572544 z^2+2239744 z^3+2309184 z^4+624960 z^5+31360 z^6
3221	311111	144+3936 z+36204 z^2+136524 z^3+206136 z^4+103320 z^5+10080 z^6	144+41904 z+705024 z^2+2389824 z^3+2150064 z^4+498960 z^5+20160 z^6
3221	2222	144+4080 z+39204 z^2+156228 z^3+253992 z^4+141960 z^5+16800 z^6	48+25488 z+546048 z^2+2209728 z^3+2341008 z^4+650160 z^5+33600 z^6
3221	22211	288+7956 z+74176 z^2+284800 z^3+441232 z^4+230464 z^5+24416 z^6	256+75456 z+1320768 z^2+4668928 z^3+4408128 z^4+1089792 z^5+48832 z^6
3221	221111	288+7620 z+67320 z^2+240888 z^3+337920 z^4+150576 z^5+11424 z^6	672+123552 z+1719360 z^2+5043840 z^3+3935520 z^4+766368 z^5+22848 z^6
3221	2111111	288+7416 z+63396 z^2+217620 z^3+288792 z^4+118584 z^5+7776 z^6	1296+169776 z+2006208 z^2+5194368 z^3+3606768 z^4+618192 z^5+15552 z^6
3221	11111111	144+3480 z+27384 z^2+83688 z^3+92352 z^4+25920 z^5	1728+145728 z+1332288 z^2+2731968 z^3+1438848 z^4+155520 z^5
32111	32111	240+6996 z+69738 z^2+292182 z^3+511590 z^4+324396 z^5+51210 z^6+630 z^7	54+31770 z+754110 z^2+3386610 z^3+4060530 z^4+1345086 z^5+98010 z^6+630 z^7
32111	311111	240+6696 z+63168 z^2+246072 z^3+388440 z^4+208296 z^5+23040 z^6	144+54000 z+1023840 z^2+3814560 z^3+3764880 z^4+973296 z^5+46080 z^6
32111	22211	240+6636 z+61944 z^2+238236 z^3+370020 z^4+194076 z^5+20736 z^6	216+62568 z+1095120 z^2+3881520 z^3+3680280 z^4+915624 z^5+41472 z^6
32111	221111	480+13044 z+119256 z^2+446964 z^3+671100 z^4+335364 z^5+33024 z^6	744+159192 z+2464560 z^2+8010960 z^3+7036200 z^4+1615896 z^5+66048 z^6
32111	2111111	480+12576 z+109824 z^2+387456 z^3+533760 z^4+231936 z^5+16896 z^6	1536+235008 z+3041280 z^2+8494080 z^3+6359040 z^4+1188864 z^5+33792 z^6
32111	11111111	240+5880 z+47040 z^2+146760 z^3+166440 z^4+48600 z^5	2160+210960 z+2086560 z^2+4548960 z^3+2536560 z^4+291600 z^5
311111	311111	720+21120 z+211920 z^2+894000 z^3+1576320 z^4+1006080 z^5+159360 z^6+1920 z^7	76800 z+2108160 z^2+10010880 z^3+12362880 z^4+4164480 z^5+305280 z^6+1920 z^7
311111	221111	720+19680 z+181200 z^2+685200 z^3+1041120 z^4+529440 z^5+53760 z^6	960+221760 z+3559680 z^2+11892480 z^3+10716480 z^4+2531520 z^5+107520 z^6
311111	2111111	1440+39120 z+357600 z^2+1340400 z^3+2013840 z^4+1008240 z^5+99840 z^6	2400+485280 z+7421760 z^2+24020160 z^3+21080160 z^4+4851360 z^5+199680 z^6
311111	11111111	720+18000 z+147600 z^2+475200 z^3+562320 z^4+174960 z^5	4320+514080 z+5676480 z^2+13538880 z^3+8246880 z^4+1049760 z^5
2222	2222	576+17328 z+179256 z^2+785640 z^3+1456800 z^4+999360 z^5+178560 z^6+2880 z^7	40320 z+1347840 z^2+7344000 z^3+10238400 z^4+3913920 z^5+336960 z^6+2880 z^7
2222	22211	576+16176 z+153816 z^2+605208 z^3+968112 z^4+529200 z^5+60480 z^6	288+118368 z+2343168 z^2+9019008 z^3+9173088 z^4+2449440 z^5+120960 z^6
2222	221111	576+15600 z+141960 z^2+528456 z^3+785040 z^4+384912 z^5+36288 z^6	864+193824 z+3006720 z^2+9694080 z^3+8382240 z^4+1874016 z^5+72576 z^6
2222	2111111	576+15216 z+134376 z^2+481848 z^3+681312 z^4+311040 z^5+25920 z^6	1728+266688 z+3509568 z^2+10041408 z^3+7797888 z^4+1555200 z^5+51840 z^6
2222	11111111	576+14928 z+128856 z^2+449160 z^3+612000 z^4+264960 z^5+20160 z^6	2880+336960 z+3913920 z^2+10238400 z^3+7344000 z^4+1347840 z^5+40320 z^6
22211	22211	720+20724 z+203508 z^2+837132 z^3+1431600 z^4+878544 z^5+131616 z^6+1440 z^7	288+118368 z+2514240 z^2+10520640 z^3+11900160 z^4+3722112 z^5+253152 z^6+1440 z^7
22211	221111	720+19764 z+182916 z^2+696204 z^3+1067040 z^4+549504 z^5+57024 z^6	864+209952 z+3460320 z^2+11797920 z^3+10834560 z^4+2612736 z^5+114048 z^6
22211	2111111	720+19224 z+172008 z^2+627192 z^3+907200 z^4+428544 z^5+38016 z^6	1728+295488 z+4121280 z^2+12363840 z^3+10056960 z^4+2115072 z^5+76032 z^6
22211	11111111	720+18840 z+164520 z^2+581880 z^3+808320 z^4+360000 z^5+28800 z^6	2880+377280 z+4639680 z^2+12674880 z^3+9463680 z^4+1814400 z^5+57600 z^6
221111	221111	1440+40848 z+394176 z^2+1586640 z^3+2637360 z^4+1554288 z^5+217632 z^6+2016 z^7	960+295488 z+5625504 z^2+21832800 z^3+23126400 z^4+6756480 z^5+421152 z^6+2016 z^7
221111	2111111	1440+39120 z+357600 z^2+1340400 z^3+2013840 z^4+1008240 z^5+99840 z^6	2400+485280 z+7421760 z^2+24020160 z^3+21080160 z^4+4851360 z^5+199680 z^6
221111	11111111	1440+38160 z+338400 z^2+1220400 z^3+1740240 z^4+805680 z^5+69120 z^6	4320+652320 z+8631360 z^2+24960960 z^3+19668960 z^4+4004640 z^5+138240 z^6
2111111	2111111	5040+141840 z+1355760 z^2+5392800 z^3+8825040 z^4+5085360 z^5+685440 z^6+5760 z^7	4320+1159200 z+20865600 z^2+77837760 z^3+79601760 z^4+22407840 z^5+1330560 z^6+5760 z^7
2111111	11111111	5040+136080 z+1234800 z^2+4586400 z^3+6809040 z^4+3351600 z^5+322560 z^6	10080+1844640 z+27034560 z^2+84893760 z^3+72545760 z^4+16238880 z^5+645120 z^6
11111111	11111111	40320+1128960 z+10725120 z^2+42336000 z^3+68584320 z^4+38949120 z^5+5120640 z^6+40320 z^7	40320+9959040 z+173093760 z^2+629758080 z^3+629758080 z^4+173093760 z^5+9959040 z^6+40320 z^7
9	9	1+72 z+2016 z^2+28224 z^3+211680 z^4+846720 z^5+1693440 z^6+1451520 z^7+362880 z^8	362880 z^8
9	81	8+504 z+12096 z^2+141120 z^3+846720 z^4+2540160 z^5+3386880 z^6+1451520 z^7	2903040 z^7
9	72	27+1512 z+31752 z^2+317520 z^3+1587600 z^4+3810240 z^5+3810240 z^6+1088640 z^7	7620480 z^6+2177280 z^7
9	711	28+1512 z+30240 z^2+282240 z^3+1270080 z^4+2540160 z^5+1693440 z^6	10160640 z^6
9	63	48+2448 z+46368 z^2+413280 z^3+1814400 z^4+3749760 z^5+3144960 z^6+725760 z^7	7257600 z^5+8709120 z^6+1451520 z^7
9	621	105+5040 z+88200 z^2+705600 z^3+2646000 z^4+4233600 z^5+2116800 z^6	25401600 z^5+12700800 z^6
9	6111	56+2520 z+40320 z^2+282240 z^3+846720 z^4+846720 z^5	20321280 z^5
9	54	42+2016 z+35784 z^2+297360 z^3+1209600 z^4+2298240 z^5+1753920 z^6+362880 z^7	1814400 z^4+7257600 z^5+5443200 z^6+725760 z^7
9	531	162+7128 z+113400 z^2+816480 z^3+2721600 z^4+3810240 z^5+1632960 z^6	16329600 z^4+32659200 z^5+9797760 z^6
9	522	120+5040 z+75600 z^2+504000 z^3+1512000 z^4+1814400 z^5+604800 z^6	18144000 z^4+21772800 z^5+3628800 z^6
9	5211	189+7560 z+105840 z^2+635040 z^3+1587600 z^4+1270080 z^5	38102400 z^4+30481920 z^5
9	51111	70+2520 z+30240 z^2+141120 z^3+211680 z^4	25401600 z^4
9	441	84+3528 z+53424 z^2+364896 z^3+1149120 z^4+1512000 z^5+604800 z^6	1451520 z^3+10886400 z^4+14515200 z^5+3628800 z^6
9	432	168+6552 z+90720 z^2+554400 z^3+1512000 z^4+1632960 z^5+483840 z^6	7257600 z^3+29030400 z^4+21772800 z^5+2903040 z^6
9	4311	216+7992 z+102816 z^2+562464 z^3+1270080 z^4+907200 z^5	13063680 z^3+43545600 z^4+21772800 z^5
9	4221	216+7560 z+90720 z^2+453600 z^3+907200 z^4+544320 z^5	21772800 z^3+43545600 z^4+13063680 z^5
9	42111	189+6048 z+63504 z^2+254016 z^3+317520 z^4	30481920 z^3+38102400 z^4
9	411111	56+1512 z+12096 z^2+28224 z^3	20321280 z^3
9	333	42+1512 z+19152 z^2+105840 z^3+257040 z^4+241920 z^5+60480 z^6	362880 z^2+3628800 z^3+7257600 z^4+3628800 z^5+362880 z^6
9	3321	168+5544 z+62496 z^2+292320 z^3+544320 z^4+302400 z^5	2903040 z^2+21772800 z^3+29030400 z^4+7257600 z^5
9	33111	120+3600 z+35280 z^2+131040 z^3+151200 z^4	3628800 z^2+21772800 z^3+18144000 z^4
9	3222	84+2520 z+25200 z^2+100800 z^3+151200 z^4+60480 z^5	3628800 z^2+14515200 z^3+10886400 z^4+1451520 z^5
9	32211	162+4536 z+40824 z^2+136080 z^3+136080 z^4	9797760 z^2+32659200 z^3+16329600 z^4
9	321111	105+2520 z+17640 z^2+35280 z^3	12700800 z^2+25401600 z^3
9	3111111	28+504 z+2016 z^2	10160640 z^2
9	22221	42+1008 z+7560 z^2+20160 z^3+15120 z^4	725760 z+5443200 z^2+7257600 z^3+1814400 z^4
9	222111	48+1008 z+6048 z^2+10080 z^3	1451520 z+8709120 z^2+7257600 z^3
9	2211111	27+432 z+1512 z^2	2177280 z+7620480 z^2
9	21111111	8+72 z	2903040 z
9	111111111	1	362880
81	81	2+121 z+2793 z^2+31458 z^3+183750 z^4+546840 z^5+758520 z^6+398160 z^7+45360 z^8	246960 z^6+433440 z^7+45360 z^8
81	72	12+642 z+12852 z^2+122220 z^3+579600 z^4+1315440 z^5+1239840 z^6+332640 z^7	907200 z^5+2782080 z^6+665280 z^7
81	711	14+742 z+14700 z^2+138180 z^3+646800 z^4+1446480 z^5+1340640 z^6+352800 z^7	1270080 z^5+3104640 z^6+705600 z^7
81	63	28+1358 z+24318 z^2+203280 z^3+827400 z^4+1557360 z^5+1154160 z^6+221760 z^7	756000 z^4+5140800 z^5+3820320 z^6+443520 z^7
81	621	70+3290 z+56700 z^2+451500 z^3+1722000 z^4+2948400 z^5+1864800 z^6+252000 z^7	3024000 z^4+14212800 z^5+7660800 z^6+504000 z^7
81	6111	42+1911 z+31605 z^2+238140 z^3+837900 z^4+1252440 z^5+582120 z^6	2646000 z^4+9102240 z^5+3492720 z^6
81	54	28+1274 z+21252 z^2+164052 z^3+609840 z^4+1033200 z^5+675360 z^6+110880 z^7	80640 z^3+2217600 z^4+5140800 z^5+2499840 z^6+221760 z^7
81	531	126+5418 z+84420 z^2+598500 z^3+1990800 z^4+2887920 z^5+1481760 z^6+151200 z^7	1209600 z^3+15120000 z^4+22317120 z^5+6773760 z^6+302400 z^7
81	522	100+4160 z+62160 z^2+416640 z^3+1276800 z^4+1612800 z^5+604800 z^6	1612800 z^3+14112000 z^4+16934400 z^5+3628800 z^6
81	5211	168+6804 z+98280 z^2+630000 z^3+1814400 z^4+2086560 z^5+665280 z^6	3628800 z^3+27216000 z^4+26127360 z^5+3991680 z^6
81	51111	70+2660 z+35280 z^2+199920 z^3+470400 z^4+352800 z^5	2822400 z^3+14112000 z^4+8467200 z^5
81	441	70+2870 z+42420 z^2+283500 z^3+882000 z^4+1184400 z^5+554400 z^6+50400 z^7	2016000 z^3+10080000 z^4+10584000 z^5+2620800 z^6+100800 z^7
81	432	154+5957 z+82005 z^2+500430 z^3+1374450 z^4+1522080 z^5+483840 z^6	226800 z^2+7812000 z^3+25830000 z^4+19111680 z^5+2903040 z^6
81	4311	210+7875 z+104265 z^2+604800 z^3+1549800 z^4+1549800 z^5+415800 z^6	453600 z^2+13608000 z^3+37422000 z^4+22226400 z^5+2494800 z^6
81	4221	222+7971 z+99855 z^2+537390 z^3+1231650 z^4+1013040 z^5+166320 z^6	1134000 z^2+18900000 z^3+41202000 z^4+18325440 z^5+997920 z^6
81	42111	210+7140 z+83160 z^2+403200 z^3+781200 z^4+453600 z^5	1814400 z^2+24192000 z^3+39312000 z^4+10886400 z^5
81	411111	70+2135 z+21315 z^2+80850 z^3+95550 z^4	1587600 z^2+12348000 z^3+11466000 z^4
81	333	42+1512 z+19152 z^2+105840 z^3+257040 z^4+241920 z^5+60480 z^6	362880 z^2+3628800 z^3+7257600 z^4+3628800 z^5+362880 z^6
81	3321	182+6181 z+72723 z^2+364308 z^3+768180 z^4+572040 z^5+83160 z^6	2903040 z^2+20885760 z^3+31021200 z^4+10735200 z^5+498960 z^6
81	33111	140+4480 z+48720 z^2+218400 z^3+386400 z^4+201600 z^5	3628800 z^2+20160000 z^3+22176000 z^4+4838400 z^5
81	3222	98+3094 z+33180 z^2+146580 z^3+255360 z^4+131040 z^5	60480 z+3024000 z^2+14414400 z^3+14918400 z^4+3144960 z^5
81	32211	198+5994 z+60732 z^2+247212 z^3+378000 z^4+151200 z^5	181440 z+7983360 z^2+32840640 z^3+27216000 z^4+3628800 z^5
81	321111	140+3850 z+34020 z^2+111300 z^3+109200 z^4	302400 z+9676800 z^2+27720000 z^3+13104000 z^4
81	3111111	42+966 z+6468 z^2+12348 z^3	423360 z+5927040 z^2+8890560 z^3
81	22221	56+1498 z+13020 z^2+43260 z^3+48720 z^4+10080 z^5	423360 z+4838400 z^2+10180800 z^3+4636800 z^4+241920 z^5
81	222111	68+1678 z+12978 z^2+35700 z^3+27300 z^4	846720 z+7953120 z^2+12600000 z^3+3276000 z^4
81	2211111	42+882 z+5292 z^2+8820 z^3	1270080 z+7620480 z^2+6350400 z^3
81	21111111	14+217 z+735 z^2	35280+1340640 z+3704400 z^2
81	111111111	2+16 z	80640+645120 z
72	72	4+210 z+4148 z^2+39292 z^3+188800 z^4+448880 z^5+477600 z^6+180960 z^7+13440 z^8	48000 z^4+427200 z^5+708480 z^6+254400 z^7+13440 z^8
72	711	4+202 z+3800 z^2+33780 z^3+148800 z^4+311280 z^5+267840 z^6+64800 z^7	72000 z^4+550080 z^5+699840 z^6+129600 z^7
72	63	16+760 z+13352 z^2+109848 z^3+442560 z^4+833280 z^5+630720 z^6+129600 z^7	34560 z^3+806400 z^4+2736000 z^5+1969920 z^6+259200 z^7
72	621	40+1840 z+31130 z^2+244740 z^3+931800 z^4+1629600 z^5+1112400 z^6+194400 z^7	172800 z^3+2772000 z^4+7228800 z^5+3952800 z^6+388800 z^7
72	6111	24+1068 z+17352 z^2+129600 z^3+460800 z^4+730080 z^5+423360 z^6+51840 z^7	172800 z^3+2160000 z^4+4458240 z^5+1814400 z^6+103680 z^7
72	54	20+890 z+14500 z^2+109140 z^3+394800 z^4+649200 z^5+410400 z^6+64800 z^7	172800 z^3+1872000 z^4+3528000 z^5+1555200 z^6+129600 z^7
72	531	96+4068 z+62550 z^2+438660 z^3+1449360 z^4+2103840 z^5+1095120 z^6+116640 z^7	25920 z^2+1814400 z^3+11858400 z^4+15966720 z^5+4937760 z^6+233280 z^7
72	522	80+3320 z+49900 z^2+341520 z^3+1101120 z^4+1568640 z^5+825120 z^6+103680 z^7	51840 z^2+2073600 z^3+10900800 z^4+12297600 z^5+3499200 z^6+207360 z^7
72	5211	136+5492 z+79668 z^2+519240 z^3+1555800 z^4+1955520 z^5+786240 z^6+34560 z^7	129600 z^2+4464000 z^3+20376000 z^4+20079360 z^5+4233600 z^6+69120 z^7
72	51111	60+2310 z+31590 z^2+190800 z^3+514800 z^4+550800 z^5+162000 z^6	129600 z^2+3024000 z^3+10260000 z^4+7387200 z^5+972000 z^6
72	441	60+2430 z+35460 z^2+233820 z^3+717120 z^4+948240 z^5+436320 z^6+38880 z^7	51840 z^2+2073600 z^3+8812800 z^4+8683200 z^5+2073600 z^6+77760 z^7
72	432	144+5592 z+77760 z^2+484560 z^3+1388160 z^4+1684800 z^5+691200 z^6+51840 z^7	414720 z^2+7603200 z^3+22982400 z^4+17729280 z^5+3421440 z^6+103680 z^7
72	4311	200+7540 z+100920 z^2+597120 z^3+1585920 z^4+1700640 z^5+544320 z^6+17280 z^7	829440 z^2+12729600 z^3+34012800 z^4+21945600 z^5+3024000 z^6+34560 z^7
72	4221	224+8208 z+106312 z^2+605000 z^3+1531040 z^4+1536160 z^5+432000 z^6	9600 z+1562880 z^2+17539200 z^3+38265600 z^4+21315840 z^5+2592000 z^6
72	42111	220+7710 z+94250 z^2+495400 z^3+1113400 z^4+911600 z^5+162000 z^6	19200 z+2400000 z^2+21600000 z^3+38796000 z^4+16046400 z^5+972000 z^6
72	411111	80+2600 z+28840 z^2+132600 z^3+242400 z^4+132000 z^5	28800 z+1785600 z^2+10800000 z^3+13248000 z^4+3168000 z^5
72	333	44+1610 z+20878 z^2+119472 z^3+306240 z^4+315120 z^5+92880 z^6	388800 z^2+3507840 z^3+7293600 z^4+4219200 z^5+557280 z^6
72	3321	200+6980 z+85360 z^2+453000 z^3+1048800 z^4+931200 z^5+216000 z^6	28800 z+2822400 z^2+20304000 z^3+33552000 z^4+14572800 z^5+1296000 z^6
72	33111	160+5320 z+61100 z^2+297600 z^3+607200 z^4+436800 z^5+64800 z^6	57600 z+3312000 z^2+19872000 z^3+26280000 z^4+8150400 z^5+388800 z^6
72	3222	116+3842 z+44128 z^2+216660 z^3+453360 z^4+349440 z^5+64800 z^6	72000 z+2805120 z^2+14472000 z^3+18302400 z^4+6053760 z^5+388800 z^6
72	32211	240+7680 z+84210 z^2+386460 z^3+723600 z^4+442800 z^5+32400 z^6	216000 z+7300800 z^2+33307200 z^3+36612000 z^4+9460800 z^5+194400 z^6
72	321111	180+5370 z+53640 z^2+215580 z^3+327000 z^4+132000 z^5	360000 z+8452800 z^2+29937600 z^3+23400000 z^4+3168000 z^5
72	3111111	60+1590 z+13500 z^2+42300 z^3+39600 z^4	388800 z+5184000 z^2+11448000 z^3+4752000 z^4
72	22221	76+2218 z+21740 z^2+86460 z^3+132720 z^4+58080 z^5	308160 z+4435200 z^2+12484800 z^3+8956800 z^4+1393920 z^5
72	222111	96+2640 z+23832 z^2+83688 z^3+103200 z^4+26400 z^5	616320 z+7315200 z^2+17055360 z^3+9216000 z^4+633600 z^5
72	2211111	64+1580 z+12258 z^2+33972 z^3+26400 z^4	7200+852480 z+7408800 z^2+11787840 z^3+3168000 z^4
72	21111111	24+492 z+2880 z^2+4680 z^3	17280+915840 z+4406400 z^2+3369600 z^3
72	111111111	4+58 z+182 z^2	30240+504000 z+917280 z^2
711	711	6+318 z+6318 z^2+59868 z^3+285300 z^4+663120 z^5+671760 z^6+228960 z^7+12960 z^8	622080 z^5+1188000 z^6+354240 z^7+12960 z^8
711	621	30+1410 z+24390 z^2+196200 z^3+765000 z^4+1371600 z^5+961200 z^6+172800 z^7	1620000 z^4+5572800 z^5+3348000 z^6+345600 z^7
711	6111	36+1680 z+28824 z^2+229680 z^3+885600 z^4+1566720 z^5+1080000 z^6+190080 z^7	2160000 z^4+6704640 z^5+3818880 z^6+380160 z^7
711	531	54+2322 z+36342 z^2+260712 z^3+888840 z^4+1354320 z^5+771120 z^6+103680 z^7	829440 z^3+6285600 z^4+9097920 z^5+3175200 z^6+207360 z^7
711	522	60+2460 z+36180 z^2+238320 z^3+716400 z^4+885600 z^5+324000 z^6	1382400 z^3+8856000 z^4+9590400 z^5+1944000 z^6
711	5211	144+6000 z+90336 z^2+616800 z^3+1968000 z^4+2724480 z^5+1324800 z^6+126720 z^7	3225600 z^3+19584000 z^4+23016960 z^5+6174720 z^6+253440 z^7
711	51111	90+3630 z+52410 z^2+338040 z^3+991800 z^4+1191600 z^5+421200 z^6	2764800 z^3+13932000 z^4+13435200 z^5+2527200 z^6
711	441	30+1230 z+18270 z^2+123660 z^3+394740 z^4+557280 z^5+289440 z^6+34560 z^7	38880 z^2+993600 z^3+4125600 z^4+4406400 z^5+1252800 z^6+69120 z^7
711	432	96+3648 z+49248 z^2+294048 z^3+787680 z^4+846720 z^5+259200 z^6	311040 z^2+5736960 z^3+16243200 z^4+10990080 z^5+1555200 z^6
711	4311	180+6960 z+96360 z^2+597840 z^3+1705440 z^4+2062080 z^5+843840 z^6+63360 z^7	622080 z^2+9907200 z^3+28713600 z^4+21772800 z^5+4176000 z^6+126720 z^7
711	4221	216+7920 z+102384 z^2+578880 z^3+1442880 z^4+1399680 z^5+362880 z^6	1244160 z^2+16588800 z^3+37843200 z^4+20528640 z^5+2177280 z^6
711	42111	270+9810 z+125550 z^2+702000 z^3+1728000 z^4+1652400 z^5+421200 z^6	1944000 z^2+22032000 z^3+46980000 z^4+24494400 z^5+2527200 z^6
711	411111	120+4080 z+47760 z^2+234720 z^3+468000 z^4+288000 z^5	1555200 z^2+13478400 z^3+21600000 z^4+6912000 z^5
711	333	30+1050 z+12870 z^2+68400 z^3+158400 z^4+140400 z^5+32400 z^6	388800 z^2+3024000 z^3+5076000 z^4+2203200 z^5+194400 z^6
711	3321	180+6240 z+75720 z^2+398160 z^3+911520 z^4+797760 z^5+181440 z^6	34560 z+2764800 z^2+18835200 z^3+29980800 z^4+12614400 z^5+1088640 z^6
711	33111	180+6180 z+74220 z^2+385920 z^3+872640 z^4+753120 z^5+168480 z^6	69120 z+3196800 z^2+19526400 z^3+29505600 z^4+12009600 z^5+1010880 z^6
711	3222	114+3690 z+40866 z^2+188460 z^3+348660 z^4+195840 z^5	69120 z+2924640 z^2+15336000 z^3+18338400 z^4+4700160 z^5
711	32211	270+8730 z+97110 z^2+455760 z^3+889920 z^4+606960 z^5+84240 z^6	207360 z+7646400 z^2+36547200 z^3+41536800 z^4+11534400 z^5+505440 z^6
711	321111	240+7440 z+78240 z^2+338400 z^3+576000 z^4+288000 z^5	345600 z+8985600 z^2+36288000 z^3+34560000 z^4+6912000 z^5
711	3111111	90+2490 z+22290 z^2+74700 z^3+76500 z^4	345600 z+6069600 z^2+17064000 z^3+9180000 z^4
711	22221	84+2412 z+23052 z^2+87912 z^3+124920 z^4+46080 z^5	345600 z+5175360 z^2+14394240 z^3+9460800 z^4+1105920 z^5
711	222111	120+3360 z+31200 z^2+115200 z^3+158400 z^4+57600 z^5	691200 z+8640000 z^2+20736000 z^3+12096000 z^4+1382400 z^5
711	2211111	90+2310 z+18930 z^2+57000 z^3+51000 z^4	7200+964800 z+9007200 z^2+16560000 z^3+6120000 z^4
711	21111111	36+768 z+4728 z^2+8208 z^3	17280+1036800 z+6099840 z^2+5909760 z^3
711	111111111	6+90 z+294 z^2	30240+665280 z+1481760 z^2
63	63	8+384 z+6870 z^2+58254 z^3+246798 z^4+506916 z^5+452628 z^6+137592 z^7+7560 z^8	216 z^2+32400 z^3+420120 z^4+1226880 z^5+1001160 z^6+214704 z^7+7560 z^8
63	621	16+720 z+11916 z^2+91704 z^3+342504 z^4+590688 z^5+402624 z^6+72576 z^7	1728 z^2+155520 z^3+1373760 z^4+2730240 z^5+1399680 z^6+145152 z^7
63	6111	8+336 z+5094 z^2+34890 z^3+110430 z^4+146520 z^5+59400 z^6	2160 z^2+151200 z^3+1015200 z^4+1378080 z^5+356400 z^6
63	54	16+720 z+11916 z^2+91704 z^3+342504 z^4+590688 z^5+402624 z^6+72576 z^7	1728 z^2+155520 z^3+1373760 z^4+2730240 z^5+1399680 z^6+145152 z^7
63	531	72+3060 z+47412 z^2+337608 z^3+1147608 z^4+1757376 z^5+1021248 z^6+145152 z^7	46656 z^2+1607040 z^3+8579520 z^4+11508480 z^5+4095360 z^6+290304 z^7
63	522	56+2292 z+33936 z^2+228336 z^3+720576 z^4+993312 z^5+487296 z^6+48384 z^7	76032 z^2+1831680 z^3+7741440 z^4+8328960 z^5+2246400 z^6+96768 z^7
63	5211	96+3840 z+55320 z^2+359952 z^3+1088832 z^4+1419264 z^5+643392 z^6+56448 z^7	186624 z^2+3893760 z^3+14302080 z^4+13271040 z^5+3070080 z^6+112896 z^7
63	51111	40+1500 z+19920 z^2+116400 z^3+302400 z^4+309600 z^5+86400 z^6	172800 z^2+2592000 z^3+6912000 z^4+4320000 z^5+518400 z^6
63	441	56+2292 z+33936 z^2+228336 z^3+720576 z^4+993312 z^5+487296 z^6+48384 z^7	76032 z^2+1831680 z^3+7741440 z^4+8328960 z^5+2246400 z^6+96768 z^7
63	432	136+5328 z+75090 z^2+477696 z^3+1414404 z^4+1816704 z^5+833760 z^6+84672 z^7	1728 z+474336 z^2+6912000 z^3+20835360 z^4+17141760 z^5+3817152 z^6+169344 z^7
63	4311	192+7320 z+99624 z^2+604470 z^3+1669614 z^4+1910376 z^5+689112 z^6+28224 z^7	5184 z+916272 z^2+11576160 z^3+31152960 z^4+22226400 z^5+3739536 z^6+56448 z^7
63	4221	216+7992 z+105138 z^2+613764 z^3+1623456 z^4+1776816 z^5+628560 z^6+36288 z^7	15552 z+1664064 z^2+16200000 z^3+35627040 z^4+21539520 z^5+3263328 z^6+72576 z^7
63	42111	216+7668 z+95688 z^2+520344 z^3+1241568 z^4+1145664 z^5+279936 z^6	31104 z+2488320 z^2+20062080 z^3+36702720 z^4+17418240 z^5+1679616 z^6
63	411111	80+2640 z+30060 z^2+144960 z^3+292320 z^4+207360 z^5+30240 z^6	34560 z+1814400 z^2+10195200 z^3+12916800 z^4+3888000 z^5+181440 z^6
63	333	48+1800 z+24180 z^2+146016 z^3+409320 z^4+499392 z^5+222912 z^6+24192 z^7	3456 z+374976 z^2+3456000 z^3+7560000 z^4+4976640 z^5+998784 z^6+48384 z^7
63	3321	224+8016 z+101412 z^2+564630 z^3+1405566 z^4+1410984 z^5+426168 z^6+12096 z^7	46656 z+2734128 z^2+20204640 z^3+36858240 z^4+19029600 z^5+2387664 z^6+24192 z^7
63	33111	184+6300 z+75240 z^2+386832 z^3+854064 z^4+696672 z^5+131328 z^6	76032 z+3196800 z^2+20010240 z^3+30706560 z^4+11992320 z^5+787968 z^6
63	3222	136+4644 z+55536 z^2+288192 z^3+653184 z^4+569952 z^5+131328 z^6	76032 z+2730240 z^2+14999040 z^3+21807360 z^4+8951040 z^5+787968 z^6
63	32211	288+9576 z+110736 z^2+549936 z^3+1173312 z^4+936576 z^5+186624 z^6	228096 z+7050240 z^2+35147520 z^3+45204480 z^4+15759360 z^5+1119744 z^6
63	321111	224+7008 z+74808 z^2+332088 z^3+595296 z^4+343008 z^5+24192 z^6	355968 z+8190720 z^2+32780160 z^3+32451840 z^4+7361280 z^5+145152 z^6
63	3111111	80+2280 z+21600 z^2+81600 z^3+115200 z^4+43200 z^5	345600 z+5184000 z^2+13824000 z^3+8640000 z^4+1036800 z^5
63	22221	104+3228 z+34368 z^2+153888 z^3+285696 z^4+184608 z^5+24192 z^6	269568 z+4389120 z^2+15068160 z^3+14307840 z^4+3559680 z^5+145152 z^6
63	222111	136+4032 z+40398 z^2+165954 z^3+268542 z^4+130896 z^5+3024 z^6	2160+517536 z+7352640 z^2+21638880 z^3+16789680 z^4+3032640 z^5+18144 z^6
63	2211111	96+2616 z+23388 z^2+81312 z^3+99480 z^4+25920 z^5	5760+720000 z+7646400 z^2+17015040 z^3+8827200 z^4+622080 z^5
63	21111111	40+960 z+7230 z^2+19470 z^3+14850 z^4	10800+756000 z+5076000 z^2+6890400 z^3+1782000 z^4
63	111111111	8+156 z+864 z^2+1320 z^3	17280+432000 z+1503360 z^2+950400 z^3
621	621	12+554 z+9454 z^2+75592 z^3+296984 z^4+551184 z^5+425328 z^6+102144 z^7+3456 z^8	75264 z^3+867360 z^4+2013120 z^5+1218720 z^6+176640 z^7+3456 z^8
621	6111	12+536 z+8776 z^2+66496 z^3+242720 z^4+404160 z^5+260160 z^6+42240 z^7	107520 z^3+1084800 z^4+2108160 z^5+969600 z^6+84480 z^7
621	531	36+1518 z+23298 z^2+163968 z^3+549120 z^4+824400 z^5+465840 z^6+63360 z^7	25920 z^2+869760 z^3+4456800 z^4+5676480 z^5+1908000 z^6+126720 z^7
621	522	48+2000 z+30292 z^2+210040 z^3+691520 z^4+1017600 z^5+561120 z^6+73920 z^7	51840 z^2+1363200 z^3+6196800 z^4+7326720 z^5+2331840 z^6+147840 z^7
621	5211	96+3936 z+58452 z^2+395376 z^3+1260120 z^4+1772640 z^5+912960 z^6+106560 z^7	129600 z^2+3150720 z^3+13204800 z^4+14152320 z^5+3985920 z^6+213120 z^7
621	51111	60+2390 z+34270 z^2+221800 z^3+666800 z^4+862800 z^5+387600 z^6+33600 z^7	129600 z^2+2544000 z^3+9012000 z^4+8164800 z^5+1855200 z^6+67200 z^7
621	441	24+964 z+13988 z^2+92144 z^3+284800 z^4+386400 z^5+190560 z^6+21120 z^7	51840 z^2+986880 z^3+3480000 z^4+3300480 z^5+847680 z^6+42240 z^7
621	432	96+3712 z+51464 z^2+320408 z^3+920176 z^4+1126128 z^5+471072 z^6+36960 z^7	1728 z+397440 z^2+5338560 z^3+15095040 z^4+11620800 z^5+2308992 z^6+73920 z^7
621	4311	156+5976 z+81984 z^2+504264 z^3+1427568 z^4+1716624 z^5+701856 z^6+53280 z^7	5184 z+777600 z^2+9334080 z^3+24750720 z^4+18169920 z^5+3465216 z^6+106560 z^7
621	4221	216+8088 z+108024 z^2+643272 z^3+1748784 z^4+1993392 z^5+754848 z^6+50400 z^7	15552 z+1503360 z^2+15099840 z^3+35055360 z^4+22783680 z^5+3823488 z^6+100800 z^7
621	42111	252+9222 z+119706 z^2+686760 z^3+1771608 z^4+1857744 z^5+594576 z^6+20160 z^7	31104 z+2280960 z^2+20016000 z^3+41764320 z^4+24027840 z^5+3285216 z^6+40320 z^7
621	411111	120+4200 z+51600 z^2+275760 z^3+645120 z^4+581760 z^5+138240 z^6	34560 z+1728000 z^2+11923200 z^3+20044800 z^4+8985600 z^5+829440 z^6
621	333	36+1302 z+16638 z^2+93384 z^3+232992 z^4+230256 z^5+63504 z^6	3456 z+354240 z^2+3041280 z^3+6043680 z^4+3240000 z^5+381024 z^6
621	3321	204+7264 z+91376 z^2+505496 z^3+1250032 z^4+1250256 z^5+385824 z^6+16800 z^7	46656 z+2643840 z^2+18880320 z^3+33521280 z^4+16822080 z^5+2079744 z^6+33600 z^7
621	33111	192+6688 z+81908 z^2+437912 z^3+1033504 z^4+962112 z^5+258528 z^6+6720 z^7	76032 z+3127680 z^2+19568640 z^3+31364160 z^4+14065920 z^5+1457088 z^6+13440 z^7
621	3222	144+4944 z+59544 z^2+312048 z^3+717984 z^4+643392 z^5+157248 z^6	76032 z+2764800 z^2+15586560 z^3+23103360 z^4+9780480 z^5+943488 z^6
621	32211	324+10914 z+128286 z^2+650736 z^3+1428912 z^4+1189296 z^5+253584 z^6	228096 z+7179840 z^2+37653120 z^3+51576480 z^4+19414080 z^5+1521504 z^6
621	321111	288+9344 z+104764 z^2+499120 z^3+1001432 z^4+718272 z^5+110592 z^6	384+352128 z+8510400 z^2+37793280 z^3+43932480 z^4+13257216 z^5+663552 z^6
621	3111111	120+3620 z+36940 z^2+154480 z^3+253040 z^4+120960 z^5	960+336000 z+5659200 z^2+18796800 z^3+15849600 z^4+2903040 z^5
621	22221	120+3744 z+40056 z^2+180000 z^3+333936 z^4+211968 z^5+24192 z^6	269568 z+4821120 z^2+17280000 z^3+16813440 z^4+4216320 z^5+145152 z^6
621	222111	168+5072 z+52000 z^2+220384 z^3+374336 z^4+202752 z^5+13824 z^6	1536+523776 z+8156160 z^2+25996800 z^3+21834240 z^4+4368384 z^5+82944 z^6
621	2211111	132+3750 z+35502 z^2+134520 z^3+191424 z^4+72576 z^5	4896+728640 z+8773920 z^2+22389120 z^3+14261760 z^4+1741824 z^5
621	21111111	60+1520 z+12280 z^2+36400 z^3+32000 z^4	9600+768000 z+6307200 z^2+10848000 z^3+3840000 z^4
621	111111111	12+246 z+1446 z^2+2376 z^3	12960+475200 z+2155680 z^2+1710720 z^3
6111	6111	24+1134 z+19788 z^2+161514 z^3+645750 z^4+1212480 z^5+935280 z^6+218160 z^7+6480 z^8	1350000 z^4+4229280 z^5+2738880 z^6+384480 z^7+6480 z^8
6111	5211	96+4056 z+62232 z^2+436416 z^3+1449120 z^4+2139840 z^5+1172160 z^6+149760 z^7	2027520 z^3+12124800 z^4+15448320 z^5+4936320 z^6+299520 z^7
6111	51111	120+5040 z+76800 z^2+534240 z^3+1756800 z^4+2563200 z^5+1382400 z^6+172800 z^7	2764800 z^3+15552000 z^4+19008000 z^5+5875200 z^6+345600 z^7
6111	4311	120+4710 z+66540 z^2+424650 z^3+1262670 z^4+1630440 z^5+751320 z^6+74880 z^7	408240 z^2+6055200 z^3+18244800 z^4+15228000 z^5+3459600 z^6+149760 z^7
6111	4221	144+5364 z+70848 z^2+412884 z^3+1076220 z^4+1121040 z^5+330480 z^6	816480 z^2+10082880 z^3+24364800 z^4+15007680 z^5+1982880 z^6
6111	42111	360+13680 z+185760 z^2+1127520 z^3+3136320 z^4+3680640 z^5+1451520 z^6+103680 z^7	1866240 z^2+22809600 z^3+58060800 z^4+40435200 z^5+7257600 z^6+207360 z^7
6111	411111	240+8820 z+114720 z^2+656820 z^3+1676700 z^4+1702800 z^5+486000 z^6	1749600 z^2+18446400 z^3+40608000 z^4+23371200 z^5+2916000 z^6
6111	3321	120+4230 z+52500 z^2+284850 z^3+682470 z^4+641160 z^5+165240 z^6	34560 z+1695600 z^2+11556000 z^3+19828800 z^4+9439200 z^5+991440 z^6
6111	33111	240+8640 z+110400 z^2+624960 z^3+1601280 z^4+1699200 z^5+587520 z^6+34560 z^7	69120 z+3041280 z^2+21081600 z^3+38707200 z^4+21081600 z^5+3041280 z^6+69120 z^7
6111	3222	96+3096 z+34152 z^2+156816 z^3+288720 z^4+161280 z^5	69120 z+2574720 z^2+13029120 z^3+15292800 z^4+3870720 z^5
6111	32211	360+12240 z+145440 z^2+747360 z^3+1667520 z^4+1416960 z^5+311040 z^6	207360 z+7257600 z^2+40435200 z^3+58060800 z^4+22809600 z^5+1866240 z^6
6111	321111	480+16200 z+190920 z^2+972000 z^3+2145600 z^4+1800000 z^5+388800 z^6	345600 z+10540800 z^2+55296000 z^3+76464000 z^4+29203200 z^5+2332800 z^6
6111	3111111	240+7560 z+81240 z^2+362160 z^3+644400 z^4+345600 z^5	345600 z+8208000 z^2+34387200 z^3+35856000 z^4+8294400 z^5
6111	22221	120+3600 z+36480 z^2+151200 z^3+244800 z^4+115200 z^5	345600 z+5875200 z^2+19008000 z^3+15552000 z^4+2764800 z^5
6111	222111	240+7380 z+77640 z^2+342180 z^3+621540 z^4+389160 z^5+48600 z^6	2160+669600 z+10681200 z^2+35596800 z^3+32259600 z^4+7590240 z^5+291600 z^6
6111	2211111	240+7080 z+70440 z^2+286080 z^3+452640 z^4+207360 z^5	5760+979200 z+13219200 z^2+38476800 z^3+29433600 z^4+4976640 z^5
6111	21111111	120+3150 z+26580 z^2+83250 z^3+78750 z^4	10800+1101600 z+10843200 z^2+22140000 z^3+9450000 z^4
6111	111111111	24+504 z+3048 z^2+5184 z^3	17280+794880 z+4164480 z^2+3732480 z^3
54	54	16+752 z+13116 z^2+107784 z^3+438840 z^4+855360 z^5+709920 z^6+192960 z^7+8640 z^8	80640 z^3+1008000 z^4+2592000 z^5+1800000 z^6+316800 z^7+8640 z^8
54	531	48+2064 z+32436 z^2+235080 z^3+817560 z^4+1291680 z^5+786240 z^6+120960 z^7	25920 z^2+950400 z^3+5400000 z^4+7776000 z^5+3024000 z^6+241920 z^7
54	522	32+1312 z+19512 z^2+132480 z^3+425520 z^4+607680 z^5+322560 z^6+40320 z^7	51840 z^2+1094400 z^3+4348800 z^4+4665600 z^5+1370880 z^6+80640 z^7
54	5211	48+1872 z+26100 z^2+162360 z^3+459000 z^4+531360 z^5+181440 z^6	129600 z^2+2332800 z^3+7646400 z^4+6220800 z^5+1088640 z^6
54	51111	16+560 z+6780 z^2+34680 z^3+72600 z^4+47520 z^5	129600 z^2+1526400 z^3+3009600 z^4+1140480 z^5
54	441	64+2720 z+42192 z^2+301320 z^3+1030320 z^4+1595520 z^5+947520 z^6+141120 z^7	51840 z^2+1497600 z^3+7574400 z^4+10108800 z^5+3709440 z^6+282240 z^7
54	432	128+5056 z+71904 z^2+461808 z^3+1379376 z^4+1777968 z^5+800352 z^6+70560 z^7	1728 z+397440 z^2+6010560 z^3+19261440 z^4+16822080 z^5+3814272 z^6+141120 z^7
54	4311	192+7488 z+104976 z^2+663264 z^3+1943568 z^4+2448144 z^5+1070496 z^6+90720 z^7	5184 z+777600 z^2+10082880 z^3+29445120 z^4+24027840 z^5+5152896 z^6+181440 z^7
54	4221	192+7104 z+93456 z^2+545472 z^3+1441584 z^4+1572912 z^5+550368 z^6+30240 z^7	15552 z+1503360 z^2+14351040 z^3+31656960 z^4+19206720 z^5+2878848 z^6+60480 z^7
54	42111	192+6816 z+85104 z^2+463464 z^3+1109088 z^4+1029024 z^5+254016 z^6	31104 z+2280960 z^2+17815680 z^3+32469120 z^4+15552000 z^5+1524096 z^6
54	411111	64+2048 z+22320 z^2+100560 z^3+179520 z^4+95040 z^5	34560 z+1728000 z^2+9043200 z^3+10137600 z^4+2280960 z^5
54	333	48+1776 z+23316 z^2+135216 z^3+351432 z^4+366336 z^5+108864 z^6	3456 z+354240 z^2+3525120 z^3+8009280 z^4+4872960 z^5+653184 z^6
54	3321	256+9344 z+121248 z^2+698544 z^3+1827792 z^4+1994256 z^5+723744 z^6+50400 z^7	46656 z+2643840 z^2+20911680 z^3+41633280 z^4+23924160 z^5+3636864 z^6+100800 z^7
54	33111	224+7936 z+99192 z^2+543552 z^3+1321104 z^4+1268352 z^5+338688 z^6	76032 z+3127680 z^2+20989440 z^3+36812160 z^4+18247680 z^5+2032128 z^6
54	3222	160+5600 z+69288 z^2+378072 z^3+929664 z^4+945792 z^5+318528 z^6+20160 z^7	76032 z+2764800 z^2+16151040 z^3+25320960 z^4+12078720 z^5+1628928 z^6+40320 z^7
54	32211	336+11376 z+134604 z^2+688968 z^3+1532952 z^4+1303776 z^5+290304 z^6	228096 z+7179840 z^2+38309760 z^3+53628480 z^4+20839680 z^5+1741824 z^6
54	321111	272+8752 z+97068 z^2+455568 z^3+893496 z^4+615168 z^5+84672 z^6	355968 z+8493120 z^2+36610560 z^3+41019840 z^4+11715840 z^5+508032 z^6
54	3111111	96+2784 z+26952 z^2+104688 z^3+153360 z^4+60480 z^5	345600 z+5616000 z^2+16277760 z^3+11145600 z^4+1451520 z^5
54	22221	144+4656 z+52332 z^2+252816 z^3+526800 z^4+415584 z^5+84672 z^6	576+263808 z+4847040 z^2+18743040 z^3+20966400 z^4+6925824 z^5+508032 z^6
54	222111	192+5952 z+63312 z^2+283488 z^3+527808 z^4+345600 z^5+48384 z^6	2304+516096 z+8190720 z^2+27901440 z^3+26219520 z^4+6552576 z^5+290304 z^6
54	2211111	144+4176 z+40716 z^2+161352 z^3+247536 z^4+108864 z^5	5184+725760 z+8786880 z^2+23483520 z^3+16640640 z^4+2612736 z^5
54	21111111	64+1664 z+14064 z^2+45648 z^3+51264 z^4+12096 z^5	9216+771840 z+6289920 z^2+11162880 z^3+4700160 z^4+290304 z^5
54	111111111	16+368 z+2652 z^2+6840 z^3+5040 z^4	14400+460800 z+2220480 z^2+2505600 z^3+604800 z^4
531	531	24+1028 z+16144 z^2+117568 z^3+415008 z^4+679184 z^5+449536 z^6+88480 z^7+2240 z^8	64 z+25280 z^2+573120 z^3+2720320 z^4+3707840 z^5+1521216 z^6+159040 z^7+2240 z^8
531	522	24+980 z+14520 z^2+98272 z^3+314944 z^4+449552 z^5+239328 z^6+30240 z^7	192 z+49920 z^2+872640 z^3+3269760 z^4+3443520 z^5+1012608 z^6+60480 z^7
531	5211	48+1936 z+28276 z^2+188136 z^3+590472 z^4+820656 z^5+421344 z^6+50400 z^7	576 z+123840 z^2+1955520 z^3+6770880 z^4+6644160 z^5+1822464 z^6+100800 z^7
531	51111	24+908 z+12228 z^2+73048 z^3+196696 z^4+214208 z^5+67392 z^6	768 z+121920 z^2+1503360 z^3+3963840 z^4+2714880 z^5+404352 z^6
531	441	24+980 z+14520 z^2+98272 z^3+314944 z^4+449552 z^5+239328 z^6+30240 z^7	192 z+49920 z^2+872640 z^3+3269760 z^4+3443520 z^5+1012608 z^6+60480 z^7
531	432	96+3776 z+53568 z^2+344320 z^3+1035904 z^4+1363712 z^5+649728 z^6+69120 z^7	3072 z+384000 z^2+4838400 z^3+14300160 z^4+12241920 z^5+2930688 z^6+138240 z^7
531	4311	144+5576 z+77696 z^2+489024 z^3+1434528 z^4+1829664 z^5+835776 z^6+83520 z^7	8064 z+748800 z^2+8196480 z^3+21957120 z^4+17331840 z^5+3845376 z^6+167040 z^7
531	4221	192+7200 z+96480 z^2+578016 z^3+1588032 z^4+1843776 z^5+722304 z^6+51840 z^7	20736 z+1451520 z^2+13374720 z^3+30689280 z^4+20424960 z^5+3608064 z^6+103680 z^7
531	42111	216+7908 z+103008 z^2+596304 z^3+1569168 z^4+1720944 z^5+621216 z^6+38880 z^7	39744 z+2194560 z^2+17340480 z^3+34974720 z^4+20571840 z^5+3182976 z^6+77760 z^7
531	411111	96+3312 z+40032 z^2+209952 z^3+480384 z^4+421632 z^5+96768 z^6	41472 z+1658880 z^2+10160640 z^3+15759360 z^4+6635520 z^5+580608 z^6
531	333	48+1816 z+24636 z^2+150296 z^3+424952 z^4+518896 z^5+225504 z^6+21600 z^7	4416 z+344640 z^2+3222720 z^3+7510080 z^4+5242560 z^5+1050624 z^6+43200 z^7
531	3321	240+8760 z+113760 z^2+656640 z^3+1723680 z^4+1887840 z^5+682560 z^6+43200 z^7	51840 z+2592000 z^2+19612800 z^3+38707200 z^4+22550400 z^5+3490560 z^6+86400 z^7
531	33111	216+7676 z+96480 z^2+534112 z^3+1323904 z^4+1326992 z^5+403488 z^6+12960 z^7	80832 z+3079680 z^2+20053440 z^3+35036160 z^4+17866560 z^5+2239488 z^6+25920 z^7
531	3222	168+5892 z+72936 z^2+396720 z^3+964080 z^4+948240 z^5+289440 z^6+12960 z^7	77760 z+2747520 z^2+16632000 z^3+27043200 z^4+12882240 z^5+1555200 z^6+25920 z^7
531	32211	384+13288 z+161872 z^2+863148 z^3+2043948 z^4+1938120 z^5+557064 z^6+21600 z^7	144+229536 z+7157520 z^2+40184640 z^3+61323120 z^4+27367776 z^5+3039984 z^6+43200 z^7
531	321111	336+11184 z+129780 z^2+649188 z^3+1403892 z^4+1148904 z^5+240408 z^6	432+348192 z+8547120 z^2+40435200 z^3+52235280 z^4+18919008 z^5+1442448 z^6
531	3111111	144+4488 z+47952 z^2+215208 z^3+399528 z^4+257040 z^5+33264 z^6	864+323136 z+5793120 z^2+20874240 z^3+20092320 z^4+4971456 z^5+199584 z^6
531	22221	168+5500 z+62664 z^2+307196 z^3+649964 z^4+520360 z^5+107352 z^6	432+246048 z+5032560 z^2+21202560 z^3+25214160 z^4+8623968 z^5+644112 z^6
531	222111	240+7656 z+84456 z^2+397008 z^3+792720 z^4+581472 z^5+102816 z^6	1728+480384 z+8579520 z^2+32555520 z^3+34603200 z^4+10253952 z^5+616896 z^6
531	2211111	192+5800 z+59620 z^2+254172 z^3+436668 z^4+241416 z^5+16632 z^6	3888+668448 z+9431280 z^2+29347200 z^3+24927120 z^4+5195232 z^5+99792 z^6
531	21111111	96+2672 z+24720 z^2+91264 z^3+126208 z^4+46592 z^5	6912+698880 z+7146240 z^2+16312320 z^3+9553920 z^4+1118208 z^5
531	111111111	24+588 z+4572 z^2+12960 z^3+10800 z^4	8640+432000 z+2825280 z^2+4147200 z^3+1296000 z^4
522	522	36+1542 z+24198 z^2+175896 z^3+618696 z^4+1006056 z^5+658152 z^6+126576 z^7+3024 z^8	32400 z^2+837216 z^3+4101840 z^4+5598720 z^5+2261520 z^6+228960 z^7+3024 z^8
522	5211	36+1470 z+21762 z^2+146988 z^3+469260 z^4+665280 z^5+349920 z^6+43200 z^7	64800 z^2+1287360 z^3+4946400 z^4+5184000 z^5+1494720 z^6+86400 z^7
522	51111	36+1434 z+20598 z^2+133956 z^3+406980 z^4+538560 z^5+254880 z^6+25920 z^7	90720 z^2+1581120 z^3+5335200 z^4+4838400 z^5+1166400 z^6+51840 z^7
522	432	72+2868 z+41304 z^2+270432 z^3+832896 z^4+1131408 z^5+564192 z^6+64800 z^7	1728 z+241920 z^2+3291840 z^3+10419840 z^4+9564480 z^5+2477952 z^6+129600 z^7
522	4311	72+2724 z+36864 z^2+223344 z^3+621648 z^4+733104 z^5+292896 z^6+21600 z^7	5184 z+466560 z^2+4726080 z^3+11473920 z^4+7957440 z^5+1454976 z^6+43200 z^7
522	4221	216+8316 z+115128 z^2+719280 z^3+2091744 z^4+2639952 z^5+1189728 z^6+116640 z^7	15552 z+1244160 z^2+12830400 z^3+33125760 z^4+25427520 z^5+5505408 z^6+233280 z^7
522	42111	216+7992 z+105408 z^2+619488 z^3+1661472 z^4+1868832 z^5+699840 z^6+46656 z^7	31104 z+1928448 z^2+16329600 z^3+34836480 z^4+21617280 z^5+3545856 z^6+93312 z^7
522	411111	144+5208 z+66864 z^2+380304 z^3+978624 z^4+1041408 z^5+359424 z^6+20736 z^7	34560 z+1686528 z^2+12337920 z^3+23362560 z^4+12925440 z^5+1866240 z^6+41472 z^7
522	333	36+1326 z+17322 z^2+99900 z^3+258012 z^4+266976 z^5+78624 z^6	3456 z+289440 z^2+2721600 z^3+6000480 z^4+3576960 z^5+471744 z^6
522	3321	216+7884 z+102384 z^2+590976 z^3+1551312 z^4+1699056 z^5+614304 z^6+38880 z^7	46656 z+2332800 z^2+17651520 z^3+34836480 z^4+20295360 z^5+3141504 z^6+77760 z^7
522	33111	180+6342 z+78942 z^2+432360 z^3+1060272 z^4+1056528 z^5+329616 z^6+15552 z^7	76032 z+2811456 z^2+17470080 z^3+29026080 z^4+14143680 z^5+1759968 z^6+31104 z^7
522	3222	216+7812 z+100644 z^2+577944 z^3+1518984 z^4+1691712 z^5+649728 z^6+51840 z^7	76032 z+2842560 z^2+18679680 z^3+34119360 z^4+19388160 z^5+3172608 z^6+103680 z^7
522	32211	432+15084 z+185676 z^2+1002048 z^3+2404488 z^4+2305800 z^5+654264 z^6+17280 z^7	144+226656 z+7380720 z^2+43410240 z^3+69516720 z^4+32511456 z^5+3683664 z^6+34560 z^7
522	321111	396+13386 z+158502 z^2+815436 z^3+1840356 z^4+1624824 z^5+410184 z^6+10368 z^7	432+351648 z+9087984 z^2+45204480 z^3+62054640 z^4+24664608 z^5+2315952 z^6+20736 z^7
522	3111111	216+7020 z+79212 z^2+383112 z^3+794376 z^4+615024 z^5+118800 z^6	864+336960 z+6743520 z^2+27889920 z^3+32214240 z^4+10483776 z^5+712800 z^6
522	22221	216+7200 z+83928 z^2+424008 z^3+935424 z^4+797400 z^5+182952 z^6	432+265248 z+5734800 z^2+25704000 z^3+33028560 z^4+12551328 z^5+1097712 z^6
522	222111	288+9216 z+101856 z^2+478224 z^3+946224 z^4+671904 z^5+104544 z^6	1728+521856 z+9823680 z^2+38845440 z^3+42327360 z^4+12362112 z^5+627264 z^6
522	2211111	252+7770 z+82134 z^2+365004 z^3+673092 z^4+434808 z^5+59400 z^6	3888+738720 z+11165040 z^2+36944640 z^3+33940080 z^4+8296992 z^5+356400 z^6
522	21111111	144+4152 z+40224 z^2+158256 z^3+240768 z^4+104832 z^5	6912+794880 z+9089280 z^2+23535360 z^3+16312320 z^4+2515968 z^5
522	111111111	36+906 z+7278 z^2+21492 z^3+18900 z^4	8640+518400 z+3866400 z^2+6402240 z^3+2268000 z^4
5211	5211	48+2008 z+30632 z^2+215056 z^3+723664 z^4+1108928 z^5+665664 z^6+110976 z^7+1920 z^8	62208 z^2+1405440 z^3+6044160 z^4+7203840 z^5+2494080 z^6+206592 z^7+1920 z^8
5211	51111	48+1944 z+28488 z^2+189936 z^3+596016 z^4+824832 z^5+418176 z^6+48384 z^7	93312 z^2+1831680 z^3+6791040 z^4+6773760 z^5+1831680 z^6+96768 z^7
5211	4311	96+3728 z+52096 z^2+328832 z^3+967232 z^4+1236544 z^5+565632 z^6+56448 z^7	3840 z+459264 z^2+5333760 z^3+14638080 z^4+11685120 z^5+2603520 z^6+112896 z^7
5211	4221	144+5520 z+76032 z^2+472128 z^3+1362624 z^4+1702848 z^5+756864 z^6+72576 z^7	11520 z+880128 z^2+8812800 z^3+22210560 z^4+16669440 z^5+3525120 z^6+145152 z^7
5211	42111	288+10884 z+147348 z^2+895416 z^3+2512536 z^4+3019872 z^5+1264896 z^6+108864 z^7	28800 z+2060352 z^2+19284480 z^3+45339840 z^4+31512960 z^5+6065280 z^6+217728 z^7
5211	411111	192+7056 z+92352 z^2+537984 z^3+1427904 z^4+1585728 z^5+584064 z^6+38016 z^7	34560 z+1893888 z^2+15102720 z^3+30965760 z^4+18627840 z^5+2972160 z^6+76032 z^7
5211	3321	144+5232 z+67584 z^2+387648 z^3+1009728 z^4+1094976 z^5+390528 z^6+24192 z^7	34560 z+1645056 z^2+12061440 z^3+23224320 z^4+13236480 z^5+2004480 z^6+48384 z^7
5211	33111	240+8652 z+110772 z^2+628848 z^3+1617984 z^4+1728000 z^5+603936 z^6+36288 z^7	72576 z+3037824 z^2+20926080 z^3+38612160 z^4+21254400 z^5+3115584 z^6+72576 z^7
5211	3222	144+5016 z+61464 z^2+328896 z^3+776160 z^4+717120 z^5+181440 z^6	69120 z+2419200 z^2+14584320 z^3+23414400 z^4+10679040 z^5+1088640 z^6
5211	32211	432+15216 z+189588 z^2+1041708 z^3+2573340 z^4+2604888 z^5+842760 z^6+44352 z^7	144+216288 z+7051536 z^2+41973120 z^3+68958000 z^4+34040736 z^5+4435632 z^6+88704 z^7
5211	321111	528+18192 z+220500 z^2+1168380 z^3+2741724 z^4+2556648 z^5+700920 z^6+19008 z^7	432+365472 z+10349424 z^2+56021760 z^3+83961360 z^4+36924768 z^5+3939408 z^6+38016 z^7
5211	3111111	288+9504 z+109224 z^2+540360 z^3+1153512 z^4+929232 z^5+190512 z^6	864+364608 z+7970400 z^2+35527680 z^3+44059680 z^4+15443136 z^5+1143072 z^6
5211	22221	192+6276 z+71304 z^2+347796 z^3+729108 z^4+573192 z^5+113400 z^6	432+272160 z+5730480 z^2+24399360 z^3+28915920 z^4+9674208 z^5+680400 z^6
5211	222111	336+10920 z+123288 z^2+597168 z^3+1242000 z^4+967392 z^5+189216 z^6	1728+549504 z+10584000 z^2+43269120 z^3+49982400 z^4+16405632 z^5+1135296 z^6
5211	2211111	336+10540 z+113768 z^2+518908 z^3+989260 z^4+667112 z^5+95256 z^6	3888+812064 z+13282800 z^2+47445120 z^3+47230800 z^4+12581472 z^5+571536 z^6
5211	21111111	192+5616 z+55344 z^2+222336 z^3+347328 z^4+156672 z^5	6912+898560 z+11162880 z^2+30965760 z^3+22878720 z^4+3760128 z^5
5211	111111111	48+1224 z+9984 z^2+30024 z^3+27000 z^4	8640+604800 z+4907520 z^2+8657280 z^3+3240000 z^4
51111	51111	120+5136 z+80184 z^2+576168 z^3+1983576 z^4+3105216 z^5+1896192 z^6+317376 z^7+5184 z^8	2359296 z^3+14207040 z^4+19301760 z^5+7079040 z^6+593280 z^7+5184 z^8
51111	42111	360+13968 z+194760 z^2+1224216 z^3+3575304 z^4+4516128 z^5+2022624 z^6+193536 z^7	1539648 z^2+19992960 z^3+55589760 z^4+43701120 z^5+9426240 z^6+387072 z^7
51111	411111	480+18528 z+256800 z^2+1602816 z^3+4641024 z^4+5799168 z^5+2559744 z^6+239616 z^7	2239488 z^2+27740160 z^3+74626560 z^4+57093120 z^5+12003840 z^6+479232 z^7
51111	33111	240+8832 z+116016 z^2+680880 z^3+1833360 z^4+2094912 z^5+821952 z^6+64512 z^7	55296 z+2526336 z^2+18881280 z^3+38073600 z^4+23397120 z^5+4028544 z^6+129024 z^7
51111	32211	360+12528 z+153288 z^2+818424 z^3+1924776 z^4+1768608 z^5+443232 z^6	165888 z+6039360 z^2+36650880 z^3+58631040 z^4+26490240 z^5+2659392 z^6
51111	321111	960+34176 z+431232 z^2+2406144 z^3+6061056 z^4+6299136 z^5+2119680 z^6+119808 z^7	387072 z+14045184 z^2+88934400 z^3+153815040 z^4+79902720 z^5+11040768 z^6+239616 z^7
51111	3111111	720+24768 z+299088 z^2+1572624 z^3+3631536 z^4+3261888 z^5+793152 z^6	442368 z+13772160 z^2+76826880 z^3+115741440 z^4+49731840 z^5+4758912 z^6
51111	22221	120+3696 z+38712 z^2+167496 z^3+287544 z^4+147456 z^5	576+270720 z+4959360 z^2+17965440 z^3+16810560 z^4+3538944 z^5
51111	222111	480+15648 z+177312 z^2+862656 z^3+1804224 z^4+1415808 z^5+279936 z^6	2304+751104 z+14757120 z^2+61286400 z^3+71804160 z^4+23901696 z^5+1679616 z^6
51111	2211111	720+23328 z+262512 z^2+1267056 z^3+2625264 z^4+2036448 z^5+396576 z^6	5184+1275264 z+23353920 z^2+93312000 z^3+106349760 z^4+34598016 z^5+2379456 z^6
51111	21111111	480+14496 z+148512 z^2+626496 z^3+1043904 z^4+516096 z^5	9216+1566720 z+23016960 z^2+73866240 z^3+63336960 z^4+12386304 z^5
51111	111111111	120+3120 z+26040 z^2+80520 z^3+75000 z^4	14400+1238400 z+11318400 z^2+21974400 z^3+9000000 z^4
441	441	48+2064 z+32532 z^2+237672 z^3+840960 z^4+1377360 z^5+909360 z^6+177120 z^7+4320 z^8	38880 z^2+1062720 z^3+5378400 z^4+7516800 z^5+3097440 z^6+319680 z^7+4320 z^8
441	432	96+3840 z+55560 z^2+365688 z^3+1133136 z^4+1550448 z^5+780192 z^6+90720 z^7	1728 z+293760 z^2+4224960 z^3+13789440 z^4+12934080 z^5+3411072 z^6+181440 z^7
441	4311	144+5688 z+81144 z^2+525528 z^3+1597968 z^4+2137104 z^5+1044576 z^6+116640 z^7	5184 z+570240 z^2+7076160 z^3+21150720 z^4+18584640 z^5+4634496 z^6+233280 z^7
441	4221	144+5400 z+72360 z^2+433512 z^3+1191024 z^4+1382832 z^5+541728 z^6+38880 z^7	15552 z+1088640 z^2+10031040 z^3+23016960 z^4+15318720 z^5+2706048 z^6+77760 z^7
441	42111	144+5184 z+65988 z^2+369360 z^3+920808 z^4+912384 z^5+254016 z^6	31104 z+1632960 z^2+12441600 z^3+23872320 z^4+12752640 z^5+1524096 z^6
441	411111	48+1560 z+17376 z^2+80784 z^3+151200 z^4+86400 z^5	34560 z+1209600 z^2+6324480 z^3+7776000 z^4+2073600 z^5
441	333	48+1776 z+23316 z^2+135216 z^3+351432 z^4+366336 z^5+108864 z^6	3456 z+354240 z^2+3525120 z^3+8009280 z^4+4872960 z^5+653184 z^6
441	3321	288+10656 z+140616 z^2+827496 z^3+2225232 z^4+2515536 z^5+951264 z^6+64800 z^7	46656 z+2643840 z^2+21798720 z^3+46241280 z^4+28848960 z^5+4800384 z^6+129600 z^7
441	33111	288+10608 z+139632 z^2+822672 z^3+2230704 z^4+2581632 z^5+1038528 z^6+86400 z^7	76032 z+3127680 z^2+22602240 z^3+45308160 z^4+28200960 z^5+5021568 z^6+172800 z^7
441	3222	192+6816 z+85704 z^2+476172 z^3+1193724 z^4+1235952 z^5+418608 z^6+25920 z^7	76032 z+2855520 z^2+18066240 z^3+30792960 z^4+15681600 z^5+2148768 z^6+51840 z^7
441	32211	432+15072 z+185412 z^2+1000668 z^3+2406588 z^4+2331000 z^5+692424 z^6+28800 z^7	144+226656 z+7445520 z^2+43683840 z^3+69372720 z^4+32226336 z^5+3751344 z^6+57600 z^7
441	321111	384+12960 z+153096 z^2+784404 z^3+1755324 z^4+1515240 z^5+349272 z^6	432+351648 z+8901360 z^2+43960320 z^3+60244560 z^4+23791968 z^5+2095632 z^6
441	3111111	144+4416 z+45996 z^2+197532 z^3+335556 z^4+169344 z^5	864+336960 z+6108480 z^2+21798720 z^3+19945440 z^4+4064256 z^5
441	22221	240+8112 z+96444 z^2+502164 z^3+1166004 z^4+1100520 z^5+331992 z^6+17280 z^7	432+265248 z+5955120 z^2+27371520 z^3+36527760 z^4+15186528 z^5+1750032 z^6+34560 z^7
441	222111	336+10968 z+124488 z^2+606960 z^3+1273104 z^4+1003104 z^5+199584 z^6	1728+521856 z+10238400 z^2+42716160 z^3+50362560 z^4+16889472 z^5+1197504 z^6
441	2211111	288+9072 z+98712 z^2+457164 z^3+898452 z^4+648648 z^5+113400 z^6	3888+738720 z+11450160 z^2+39968640 z^3+40182480 z^4+11485152 z^5+680400 z^6
441	21111111	144+4152 z+40224 z^2+158256 z^3+240768 z^4+104832 z^5	6912+794880 z+9089280 z^2+23535360 z^3+16312320 z^4+2515968 z^5
441	111111111	48+1296 z+11604 z^2+41400 z^3+55440 z^4+20160 z^5	8640+518400 z+4138560 z^2+8035200 z^3+4233600 z^4+483840 z^5
432	432	72+2928 z+43314 z^2+294012 z^3+953136 z^4+1401048 z^5+802872 z^6+127440 z^7+2160 z^8	1728 z+209520 z^2+2890080 z^3+9739440 z^4+9953280 z^5+3093552 z^6+237600 z^7+2160 z^8
432	4311	72+2784 z+38754 z^2+243864 z^3+716148 z^4+916704 z^5+422496 z^6+43200 z^7	5184 z+401760 z^2+4164480 z^3+10933920 z^4+8605440 z^5+1930176 z^6+86400 z^7
432	4221	144+5496 z+75372 z^2+466062 z^3+1340094 z^4+1670472 z^5+742968 z^6+72000 z^7	15552 z+978480 z^2+9116640 z^3+22181760 z^4+16368480 z^5+3449808 z^6+144000 z^7
432	42111	144+5280 z+68964 z^2+401064 z^3+1063488 z^4+1181664 z^5+436896 z^6+28800 z^7	31104 z+1503360 z^2+11479680 z^3+23123520 z^4+13841280 z^5+2218176 z^6+57600 z^7
432	411111	72+2496 z+30390 z^2+161190 z^3+375570 z^4+340200 z^5+83160 z^6	34560 z+1242000 z^2+7452000 z^3+11728800 z^4+5171040 z^5+498960 z^6
432	333	72+2820 z+39840 z^2+255096 z^3+765072 z^4+1005696 z^5+480384 z^6+51840 z^7	3456 z+328320 z^2+3784320 z^3+10730880 z^4+9020160 z^5+2156544 z^6+103680 z^7
432	3321	288+10800 z+145060 z^2+874590 z^3+2435834 z^4+2909884 z^5+1216324 z^6+105920 z^7	8+46576 z+2436840 z^2+20332160 z^3+45168760 z^4+30498192 z^5+5815064 z^6+211840 z^7
432	33111	216+7764 z+99100 z^2+560808 z^3+1438232 z^4+1531024 z^5+533488 z^6+32000 z^7	32+75712 z+2869920 z^2+19097600 z^3+34638880 z^4+18883008 z^5+2752928 z^6+64000 z^7
432	3222	216+7764 z+99100 z^2+560808 z^3+1438232 z^4+1531024 z^5+533488 z^6+32000 z^7	32+75712 z+2869920 z^2+19097600 z^3+34638880 z^4+18883008 z^5+2752928 z^6+64000 z^7
432	32211	504+17940 z+226452 z^2+1264992 z^3+3194160 z^4+3334848 z^5+1132224 z^6+65280 z^7	192+226176 z+7525440 z^2+46663680 z^3+80448000 z^4+42018048 z^5+5879424 z^6+130560 z^7
432	321111	432+14784 z+177916 z^2+936024 z^3+2183744 z^4+2037280 z^5+576352 z^6+22400 z^7	512+350848 z+9164160 z^2+47093120 z^3+67879360 z^4+29086848 z^5+3144512 z^6+44800 z^7
432	3111111	216+7020 z+79212 z^2+383112 z^3+794376 z^4+615024 z^5+118800 z^6	864+336960 z+6743520 z^2+27889920 z^3+32214240 z^4+10483776 z^5+712800 z^6
432	22221	288+9840 z+118384 z^2+624336 z^3+1468784 z^4+1402240 z^5+425152 z^6+22400 z^7	512+264448 z+6399360 z^2+31592960 z^3+44680960 z^4+19289088 z^5+2237312 z^6+44800 z^7
432	222111	432+14472 z+169816 z^2+865944 z^3+1938416 z^4+1699432 z^5+424984 z^6+8960 z^7	1616+522976 z+11101680 z^2+50532800 z^3+66299440 z^4+25863264 z^5+2424464 z^6+17920 z^7
432	2211111	360+11532 z+128016 z^2+607608 z^3+1232064 z^4+927936 z^5+172800 z^6	3456+743040 z+12700800 z^2+48055680 z^3+52047360 z^4+16049664 z^5+1036800 z^6
432	21111111	216+6552 z+67950 z^2+295074 z^3+528138 z^4+326412 z^5+40500 z^6	5832+805680 z+10673640 z^2+32425920 z^3+27852120 z^4+6375888 z^5+243000 z^6
432	111111111	72+2028 z+19128 z^2+72936 z^3+106848 z^4+44352 z^5	6912+535680 z+5149440 z^2+11871360 z^3+7499520 z^4+1064448 z^5
4311	4311	96+3832 z+55460 z^2+366652 z^3+1150060 z^4+1618760 z^5+872040 z^6+125040 z^7+1680 z^8	3840 z+369840 z^2+4476960 z^3+13604400 z^4+12614400 z^5+3528720 z^6+236640 z^7+1680 z^8
4311	4221	96+3640 z+49524 z^2+303220 z^3+860780 z^4+1054320 z^5+456720 z^6+42240 z^7	11520 z+701280 z^2+6331200 z^3+14923200 z^4+10635840 z^5+2148960 z^6+84480 z^7
4311	42111	192+7216 z+97176 z^2+587776 z^3+1643840 z^4+1975200 z^5+833280 z^6+73920 z^7	28800 z+1578240 z^2+13384320 z^3+30057600 z^4+20511360 z^5+3964800 z^6+147840 z^7
4311	411111	96+3384 z+42036 z^2+228564 z^3+549900 z^4+520560 z^5+136080 z^6	34560 z+1404000 z^2+9218880 z^3+15768000 z^4+7594560 z^5+816480 z^6
4311	3321	192+7184 z+96272 z^2+579124 z^3+1609552 z^4+1919908 z^5+802780 z^6+70400 z^7	8+34480 z+1695960 z^2+13756640 z^3+30079480 z^4+20134512 z^5+3831080 z^6+140800 z^7
4311	33111	288+10640 z+140528 z^2+831112 z^3+2263240 z^4+2631568 z^5+1063504 z^6+88640 z^7	32+72256 z+3008160 z^2+22206080 z^3+45311200 z^4+28594368 z^5+5140064 z^6+177280 z^7
4311	3222	192+6896 z+87944 z^2+497176 z^3+1273528 z^4+1353712 z^5+470800 z^6+28160 z^7	32+68800 z+2576160 z^2+17039360 z^3+30778720 z^4+16723008 z^5+2430560 z^6+56320 z^7
4311	32211	480+17088 z+215736 z^2+1205424 z^3+3044784 z^4+3180480 z^5+1080672 z^6+62400 z^7	192+215808 z+7162560 z^2+44411520 z^3+76608960 z^4+40048128 z^5+5610432 z^6+124800 z^7
4311	321111	576+20144 z+249080 z^2+1357408 z^3+3323872 z^4+3333664 z^5+1068928 z^6+56000 z^7	512+364672 z+10321920 z^2+57603200 z^3+91108480 z^4+43878528 z^5+5629568 z^6+112000 z^7
4311	3111111	288+9504 z+109224 z^2+540360 z^3+1153512 z^4+929232 z^5+190512 z^6	864+364608 z+7970400 z^2+35527680 z^3+44059680 z^4+15443136 z^5+1143072 z^6
4311	22221	288+9776 z+116528 z^2+606016 z^3+1393408 z^4+1274752 z^5+350080 z^6+12800 z^7	512+271360 z+6589440 z^2+32322560 z^3+44849920 z^4+18528768 z^5+1921280 z^6+25600 z^7
4311	222111	480+16184 z+191588 z^2+989692 z^3+2262412 z^4+2064280 z^5+571816 z^6+22400 z^7	1616+550624 z+11900880 z^2+54997760 z^3+73671280 z^4+29898144 z^5+3117296 z^6+44800 z^7
4311	2211111	480+15664 z+177968 z^2+870592 z^3+1840192 z^4+1474880 z^5+305856 z^6	3456+816384 z+14974080 z^2+60802560 z^3+71364480 z^4+24386304 z^5+1835136 z^6
4311	21111111	288+8856 z+93348 z^2+413496 z^3+758988 z^4+485172 z^5+63180 z^6	5832+909360 z+13038840 z^2+42262560 z^3+38544120 z^4+9369648 z^5+379080 z^6
4311	111111111	96+2736 z+26160 z^2+101376 z^3+151488 z^4+64512 z^5	6912+622080 z+6462720 z^2+15759360 z^3+10437120 z^4+1548288 z^5
4221	4221	144+5652 z+80222 z^2+518262 z^3+1580450 z^4+2145920 z^5+1100400 z^6+146160 z^7+1680 z^8	9600 z+720480 z^2+7642560 z^3+21066000 z^4+17932320 z^5+4603200 z^6+278880 z^7+1680 z^8
4221	42111	144+5436 z+73580 z^2+447744 z^3+1261424 z^4+1529888 z^5+653664 z^6+59136 z^7	19200 z+1114368 z^2+9765120 z^3+22474560 z^4+15669120 z^5+3094080 z^6+118272 z^7
4221	411111	144+5316 z+70050 z^2+412314 z^3+1112694 z^4+1271928 z^5+496584 z^6+38016 z^7	28800 z+1426608 z^2+11106720 z^3+22923360 z^4+14245920 z^5+2447280 z^6+76032 z^7
4221	3321	144+5364 z+71510 z^2+427514 z^3+1179162 z^4+1392748 z^5+574420 z^6+49280 z^7	8+28720 z+1345320 z^2+10591040 z^3+22617880 z^4+14816592 z^5+2756600 z^6+98560 z^7
4221	33111	144+5148 z+65300 z^2+366824 z^3+932376 z^4+981328 z^5+336688 z^6+19712 z^7	32+57280 z+2038176 z^2+13068800 z^3+23047840 z^4+12259008 z^5+1744160 z^6+39424 z^7
4221	3222	288+10632 z+140276 z^2+828392 z^3+2250888 z^4+2608192 z^5+1047760 z^6+86240 z^7	32+71680 z+3013920 z^2+22287680 z^3+45385120 z^4+28499328 z^5+5079200 z^6+172480 z^7
4221	32211	576+20856 z+268980 z^2+1545456 z^3+4057488 z^4+4492752 z^5+1690080 z^6+124320 z^7	192+214080 z+7490880 z^2+49287360 z^3+91173120 z^4+52204608 z^5+8400000 z^6+248640 z^7
4221	321111	576+20184 z+250172 z^2+1367408 z^3+3361200 z^4+3388816 z^5+1095232 z^6+58208 z^7	512+354880 z+10139904 z^2+57120320 z^3+91182400 z^4+44347968 z^5+5756480 z^6+116416 z^7
4221	3111111	432+14832 z+179460 z^2+952632 z^3+2256696 z^4+2165184 z^5+650160 z^6+30240 z^7	864+380160 z+9214560 z^2+46422720 z^3+67379040 z^4+29828736 z^5+3477600 z^6+60480 z^7
4221	22221	432+15036 z+184904 z^2+1001216 z^3+2432688 z^4+2415952 z^5+764320 z^6+39200 z^7	512+303040 z+8138880 z^2+44039360 z^3+68053120 z^4+32113728 z^5+4037120 z^6+78400 z^7
4221	222111	576+19488 z+231392 z^2+1197248 z^3+2730984 z^4+2458216 z^5+642040 z^6+15680 z^7	1616+600160 z+13621680 z^2+65170880 z^3+89418160 z^4+36542304 z^5+3632720 z^6+31360 z^7
4221	2211111	576+18948 z+217512 z^2+1079328 z^3+2332464 z^4+1949616 z^5+456480 z^6+10080 z^7	3456+889920 z+17038080 z^2+71369280 z^3+86319360 z^4+30780864 z^5+2597760 z^6+20160 z^7
4221	21111111	432+13716 z+150714 z^2+706806 z^3+1412478 z^4+1044252 z^5+189540 z^6	5832+1030320 z+16319880 z^2+58786560 z^3+61245720 z^4+18238608 z^5+1137240 z^6
4221	111111111	144+4200 z+41304 z^2+165840 z^3+259728 z^4+118272 z^5	6912+737280 z+8576640 z^2+23120640 z^3+16974720 z^4+2838528 z^5
42111	42111	240+9324 z+130716 z^2+831624 z^3+2486376 z^4+3285984 z^5+1618368 z^6+200256 z^7+1920 z^8	18816 z+1351488 z^2+13651200 z^3+35816640 z^4+28905600 z^5+6960384 z^6+385152 z^7+1920 z^8
42111	411111	240+9024 z+121536 z^2+734784 z^3+2052096 z^4+2457984 z^5+1029888 z^6+89856 z^7	32256 z+1916928 z^2+16657920 z^3+37693440 z^4+25689600 z^5+4921344 z^6+179712 z^7
42111	33111	240+8844 z+116388 z^2+684816 z^3+1850784 z^4+2126784 z^5+842400 z^6+67392 z^7	56448 z+2514816 z^2+18748800 z^3+37978560 z^4+23546880 z^5+4110912 z^6+134784 z^7
42111	32211	480+17448 z+226092 z^2+1306716 z^3+3457164 z^4+3869208 z^5+1479816 z^6+112320 z^7	144+167904 z+6011280 z^2+40291200 z^3+75875760 z^4+44305056 z^5+7306416 z^6+224640 z^7
42111	321111	960+34440 z+439308 z^2+2490252 z^3+6426348 z^4+6951720 z^5+2525688 z^6+174528 z^7	432+418464 z+13707504 z^2+85881600 z^3+152050320 z^4+83246688 z^5+12710736 z^6+349056 z^7
42111	3111111	720+25128 z+310032 z^2+1685736 z^3+4118184 z^4+4120848 z^5+1318896 z^6+69120 z^7	864+489024 z+13258080 z^2+72576000 z^3+113542560 z^4+54323136 z^5+6945696 z^6+138240 z^7
42111	22221	240+8124 z+96336 z^2+496068 z^3+1117572 z^4+973704 z^5+227448 z^6	432+221472 z+5459760 z^2+27129600 z^3+37734480 z^4+15180768 z^5+1364688 z^6
42111	222111	720+24696 z+298584 z^2+1584432 z^3+3755088 z^4+3610656 z^5+1091232 z^6+51840 z^7	1728+667008 z+15629760 z^2+77587200 z^3+111913920 z^4+49548672 z^5+5821632 z^6+103680 z^7
42111	2211111	960+32196 z+378384 z^2+1933932 z^3+4344828 z^4+3834216 z^5+974232 z^6+23040 z^7	3888+1163808 z+24539760 z^2+111830400 z^3+147341520 z^4+57916512 z^5+5522832 z^6+46080 z^7
42111	21111111	720+23184 z+259056 z^2+1240128 z^3+2544192 z^4+1949184 z^5+373248 z^6	6912+1423872 z+24572160 z^2+94694400 z^3+104993280 z^4+33343488 z^5+2239488 z^6
42111	111111111	240+7080 z+70560 z^2+287880 z^3+459960 z^4+215040 z^5	8640+1065600 z+13363200 z^2+38102400 z^3+29390400 z^4+5160960 z^5
411111	411111	720+28440 z+405720 z^2+2629080 z^3+8014320 z^4+10809720 z^5+5435640 z^6+684720 z^7+6480 z^8	2624400 z^2+35687520 z^3+106282800 z^4+92145600 z^5+23209200 z^6+1317600 z^7+6480 z^8
411111	321111	1440+52560 z+684000 z^2+3970800 z^3+10553040 z^4+11862720 z^5+4553280 z^6+345600 z^7	414720 z+16848000 z^2+118368000 z^3+228441600 z^4+135302400 z^5+22481280 z^6+691200 z^7
411111	3111111	2160+78480 z+1015920 z^2+5860800 z^3+15456960 z^4+17205120 z^5+6514560 z^6+483840 z^7	691200 z+26680320 z^2+181785600 z^3+342662400 z^4+198720000 z^5+32313600 z^6+967680 z^7
411111	222111	720+24120 z+282600 z^2+1434600 z^3+3175920 z^4+2705400 z^5+612360 z^6	2160+807840 z+18046800 z^2+84283200 z^3+111574800 z^4+42884640 z^5+3674160 z^6
411111	2211111	2160+74160 z+897840 z^2+4773600 z^3+11345760 z^4+10958400 z^5+3337920 z^6+161280 z^7	5760+2016000 z+46707840 z^2+231782400 z^3+335606400 z^4+149610240 z^5+17769600 z^6+322560 z^7
411111	21111111	2160+71640 z+829800 z^2+4156200 z^3+9052560 z^4+7553880 z^5+1662120 z^6	10800+2933280 z+59302800 z^2+260712000 z^3+329432400 z^4+121456800 z^5+9972720 z^6
411111	111111111	720+21600 z+219600 z^2+918000 z^3+1512720 z^4+737280 z^5	17280+2592000 z+36115200 z^2+111801600 z^3+93052800 z^4+17694720 z^5
333	333	216+8964 z+135588 z^2+943416 z^3+3145320 z^4+4776480 z^5+2846880 z^6+475200 z^7+8640 z^8	362880 z^2+7015680 z^3+27820800 z^4+31622400 z^5+10670400 z^6+881280 z^7+8640 z^8
333	3321	432+16632 z+230352 z^2+1440720 z^3+4199040 z^4+5322240 z^5+2419200 z^6+241920 z^7	34560 z+2557440 z^2+25747200 z^3+66009600 z^4+50803200 z^5+11128320 z^6+483840 z^7
333	33111	216+7668 z+96060 z^2+527760 z^3+1286640 z^4+1239840 z^5+332640 z^6	69120 z+2937600 z^2+20044800 z^3+35553600 z^4+17781120 z^5+1995840 z^6
333	3222	216+7668 z+96060 z^2+527760 z^3+1286640 z^4+1239840 z^5+332640 z^6	69120 z+2937600 z^2+20044800 z^3+35553600 z^4+17781120 z^5+1995840 z^6
333	32211	648+23652 z+307944 z^2+1789812 z^3+4767876 z^4+5383224 z^5+2084040 z^6+161280 z^7	144+205920 z+7730640 z^2+53262720 z^3+102432240 z^4+60945696 z^5+10246320 z^6+322560 z^7
333	321111	432+14688 z+174948 z^2+904716 z^3+2045628 z^4+1785672 z^5+415800 z^6	432+341280 z+9264240 z^2+48159360 z^3+68616720 z^4+27887328 z^5+2494800 z^6
333	3111111	216+7020 z+79212 z^2+383112 z^3+794376 z^4+615024 z^5+118800 z^6	864+336960 z+6743520 z^2+27889920 z^3+32214240 z^4+10483776 z^5+712800 z^6
333	22221	432+14688 z+174948 z^2+904716 z^3+2045628 z^4+1785672 z^5+415800 z^6	432+341280 z+9264240 z^2+48159360 z^3+68616720 z^4+27887328 z^5+2494800 z^6
333	222111	864+30240 z+375240 z^2+2061792 z^3+5134032 z^4+5328288 z^5+1844640 z^6+120960 z^7	1728+673920 z+16390080 z^2+86054400 z^3+134239680 z^4+66552192 z^5+9374400 z^6+241920 z^7
333	2211111	648+21276 z+243432 z^2+1200636 z^3+2562732 z^4+2078568 z^5+437400 z^6	3888+997920 z+19200240 z^2+80714880 z^3+97465680 z^4+34139232 z^5+2624400 z^6
333	21111111	432+13608 z+148128 z^2+686736 z^3+1352448 z^4+980352 z^5+172800 z^6	6912+1140480 z+17245440 z^2+59823360 z^3+60203520 z^4+17307648 z^5+1036800 z^6
333	111111111	216+6588 z+69060 z^2+306000 z^3+569520 z^4+383040 z^5+60480 z^6	8640+881280 z+10670400 z^2+31622400 z^3+27820800 z^4+7015680 z^5+362880 z^6
3321	3321	288+11088 z+153928 z^2+968868 z^3+2862872 z^4+3735148 z^5+1814500 z^6+221840 z^7+2160 z^8	8+34480 z+1922760 z^2+17509760 z^3+43254280 z^4+33517872 z^5+7841720 z^6+426400 z^7+2160 z^8
3321	33111	288+10656 z+140968 z^2+835176 z^3+2278568 z^4+2654512 z^5+1074640 z^6+89600 z^7	32+68800 z+2939040 z^2+22012160 z^3+45332320 z^4+28784448 z^5+5193440 z^6+179200 z^7
3321	3222	288+10656 z+140968 z^2+835176 z^3+2278568 z^4+2654512 z^5+1074640 z^6+89600 z^7	32+68800 z+2939040 z^2+22012160 z^3+45332320 z^4+28784448 z^5+5193440 z^6+179200 z^7
3321	32211	576+20928 z+271056 z^2+1565808 z^3+4140528 z^4+4631712 z^5+1770720 z^6+134400 z^7	192+205440 z+7266240 z^2+48460800 z^3+91014720 z^4+53059968 z^5+8742720 z^6+268800 z^7
3321	321111	576+20256 z+252160 z^2+1385856 z^3+3431168 z^4+3494272 z^5+1146880 z^6+62720 z^7	512+340480 z+9838080 z^2+56245760 z^3+91256320 z^4+45209088 z^5+6003200 z^6+125440 z^7
3321	3111111	288+9600 z+111768 z^2+562680 z^3+1231416 z^4+1031184 z^5+226800 z^6	864+336960 z+7469280 z^2+34318080 z^3+44439840 z^4+16583616 z^5+1360800 z^6
3321	22221	576+20256 z+252160 z^2+1385856 z^3+3431168 z^4+3494272 z^5+1146880 z^6+62720 z^7	512+340480 z+9838080 z^2+56245760 z^3+91256320 z^4+45209088 z^5+6003200 z^6+125440 z^7
3321	222111	864+30072 z+370300 z^2+2012484 z^3+4929860 z^4+4983928 z^5+1646536 z^6+97664 z^7	1616+675040 z+16789392 z^2+88050560 z^3+134863600 z^4+64440864 z^5+8511920 z^6+195328 z^7
3321	2211111	864+29232 z+347760 z^2+1809504 z^3+4183200 z^4+3889728 z^5+1118016 z^6+48384 z^7	3456+1002240 z+21140352 z^2+97666560 z^3+132451200 z^4+55137024 z^5+6030720 z^6+96768 z^7
3321	21111111	576+18576 z+208080 z^2+1000116 z^3+2065968 z^4+1603332 z^5+315900 z^6	5832+1151280 z+19600920 z^2+75310560 z^3+83947320 z^4+27107568 z^5+1895400 z^6
3321	111111111	288+8976 z+96528 z^2+441216 z^3+854208 z^4+605952 z^5+103680 z^6	6912+898560 z+12407040 z^2+40642560 z^3+39121920 z^4+10810368 z^5+622080 z^6
33111	33111	480+18432 z+255000 z^2+1597536 z^3+4689288 z^4+6057432 z^5+2894616 z^6+342576 z^7+3024 z^8	55296 z+3237840 z^2+29608416 z^3+72569520 z^4+55391040 z^5+12656304 z^6+660960 z^7+3024 z^8
33111	32211	480+17472 z+226776 z^2+1313328 z^3+3483672 z^4+3912552 z^5+1504152 z^6+115200 z^7	144+164448 z+5929200 z^2+40011840 z^3+75844080 z^4+44590176 z^5+7412112 z^6+230400 z^7
33111	321111	960+34704 z+446856 z^2+2563488 z^3+6721272 z^4+7436664 z^5+2800008 z^6+207360 z^7	432+382752 z+12828240 z^2+82814400 z^3+151638480 z^4+86388768 z^5+13897008 z^6+414720 z^7
33111	3111111	480+16272 z+193296 z^2+997488 z^3+2253312 z^4+1970352 z^5+462672 z^6	864+433728 z+10778400 z^2+53965440 z^3+75595680 z^4+30632256 z^5+2776032 z^6
33111	22221	480+16992 z+213384 z^2+1186992 z^3+2991528 z^4+3135672 z^5+1087560 z^6+69120 z^7	432+272160 z+7868880 z^2+45593280 z^3+75744720 z^4+39007008 z^5+5557680 z^6+138240 z^7
33111	222111	960+33264 z+407040 z^2+2191824 z^3+5291856 z^4+5216544 z^5+1635552 z^6+82944 z^7	1728+756864 z+19023552 z^2+99532800 z^3+150431040 z^4+69800832 z^5+8652096 z^6+165888 z^7
33111	2211111	1440+49824 z+609480 z^2+3287664 z^3+7984296 z^4+7989624 z^5+2606472 z^6+152064 z^7	3888+1288224 z+29804112 z^2+150033600 z^3+223298640 z^4+104304672 z^5+13509936 z^6+304128 z^7
33111	21111111	960+31392 z+357504 z^2+1753632 z^3+3718368 z^4+2990592 z^5+622080 z^6	6912+1589760 z+29445120 z^2+120890880 z^3+143320320 z^4+49379328 z^5+3732480 z^6
33111	111111111	480+15120 z+164640 z^2+763920 z^3+1506960 z^4+1095840 z^5+194400 z^6	8640+1296000 z+19224000 z^2+66355200 z^3+66830400 z^4+19301760 z^5+1166400 z^6
3222	3222	576+22224 z+309216 z^2+1950804 z^3+5777820 z^4+7554960 z^5+3676320 z^6+449280 z^7+4320 z^8	60480 z+3672000 z^2+34464960 z^3+86464800 z^4+67599360 z^5+15888960 z^6+864000 z^7+4320 z^8
3222	32211	576+21072 z+275136 z^2+1605012 z^3+4296756 z^4+4885704 z^5+1912680 z^6+151200 z^7	144+180000 z+6745680 z^2+46797120 z^3+90883440 z^4+54750816 z^5+9359280 z^6+302400 z^7
3222	321111	576+20496 z+258960 z^2+1451196 z^3+3691548 z^4+3917592 z^5+1383480 z^6+90720 z^7	432+298080 z+8970480 z^2+53472960 z^3+91037520 z^4+48027168 z^5+7030800 z^6+181440 z^7
3222	3111111	576+20112 z+248496 z^2+1355292 z^3+3331476 z^4+3376944 z^5+1114560 z^6+64800 z^7	864+414720 z+10774080 z^2+57957120 z^3+90318240 z^4+43644096 z^5+5780160 z^6+129600 z^7
3222	22221	1152+41856 z+542184 z^2+3133116 z^3+8290908 z^4+9287352 z^5+3560760 z^6+272160 z^7	432+419040 z+14603760 z^2+96932160 z^3+181843920 z^4+106139808 z^5+17554320 z^6+544320 z^7
3222	222111	1152+40128 z+494088 z^2+2680560 z^3+6532848 z^4+6520320 z^5+2081376 z^6+108864 z^7	1728+829440 z+21719232 z^2+116968320 z^3+181206720 z^4+86130432 z^5+10964160 z^6+217728 z^7
3222	2211111	1152+39168 z+468648 z^2+2455380 z^3+5725188 z^4+5383800 z^5+1572696 z^6+69984 z^7	3888+1231200 z+26991792 z^2+128070720 z^3+177610320 z^4+75533472 z^5+8456400 z^6+139968 z^7
3222	21111111	1152+38496 z+451344 z^2+2307456 z^3+5217408 z^4+4709952 z^5+1296000 z^6+51840 z^7	6912+1624320 z+31276800 z^2+135509760 z^3+173905920 z^4+68560128 z^5+7050240 z^6+103680 z^7
3222	111111111	576+18384 z+203496 z^2+964584 z^3+1959480 z^4+1488960 z^5+285120 z^6	8640+1365120 z+21254400 z^2+77086080 z^3+82123200 z^4+25470720 z^5+1710720 z^6
32211	32211	720+26868 z+359648 z^2+2167132 z^3+6066588 z^4+7375928 z^5+3242632 z^6+336448 z^7+2240 z^8	144+177760 z+7110224 z^2+52905600 z^3+111321520 z^4+74292896 z^5+14808240 z^6+654976 z^7+2240 z^8
32211	321111	720+25908 z+331824 z^2+1891644 z^3+4921836 z^4+5392488 z^5+2002968 z^6+145152 z^7	432+318240 z+10137456 z^2+63504000 z^3+113628240 z^4+63409248 z^5+9985680 z^6+290304 z^7
32211	3111111	720+25368 z+316848 z^2+1751352 z^3+4379928 z^4+4546128 z^5+1555632 z^6+96768 z^7	864+452160 z+12413664 z^2+69776640 z^3+113289120 z^4+57168576 z^5+7979040 z^6+193536 z^7
32211	22221	720+25908 z+331824 z^2+1891644 z^3+4921836 z^4+5392488 z^5+2002968 z^6+145152 z^7	432+318240 z+10137456 z^2+63504000 z^3+113628240 z^4+63409248 z^5+9985680 z^6+290304 z^7
32211	222111	1440+50952 z+639816 z^2+3561456 z^3+8993424 z^4+9470112 z^5+3320352 z^6+217728 z^7	1728+869760 z+24053184 z^2+137030400 z^3+226388160 z^4+116894592 z^5+16873920 z^6+435456 z^7
32211	2211111	1440+49452 z+598896 z^2+3185556 z^3+7575924 z^4+7323912 z^5+2234232 z^6+108288 z^7	3888+1343520 z+31094064 z^2+154368000 z^3+223742160 z^4+99889632 z^5+11889360 z^6+216576 z^7
32211	21111111	1440+48528 z+574704 z^2+2974464 z^3+6831936 z^4+6300288 z^5+1790208 z^6+76032 z^7	6912+1797120 z+36516096 z^2+164851200 z^3+219594240 z^4+89952768 z^5+9676800 z^6+152064 z^7
32211	111111111	720+23160 z+258720 z^2+1239960 z^3+2553960 z^4+1976640 z^5+388800 z^6	8640+1526400 z+25084800 z^2+94608000 z^3+104270400 z^4+33442560 z^5+2332800 z^6
321111	321111	1440+53328 z+707424 z^2+4216176 z^3+11639760 z^4+13891008 z^5+5942208 z^6+587904 z^7+3456 z^8	384+410880 z+15465600 z^2+110298624 z^3+223737600 z^4+143963136 z^5+27519360 z^6+1148160 z^7+3456 z^8
321111	3111111	1440+51600 z+657600 z^2+3726000 z^3+9619440 z^4+10428960 z^5+3813600 z^6+268800 z^7	960+681600 z+21124800 z^2+129523200 z^3+227265600 z^4+124295040 z^5+19118400 z^6+537600 z^7
321111	222111	1440+51168 z+645792 z^2+3617280 z^3+9208320 z^4+9804288 z^5+3495936 z^6+236544 z^7	1536+814080 z+23127552 z^2+134522880 z^3+226560000 z^4+119384064 z^5+17664000 z^6+473088 z^7
321111	2211111	2880+101088 z+1257552 z^2+6922080 z^3+17238960 z^4+17826768 z^5+6091056 z^6+382464 z^7	4896+2024640 z+52127712 z^2+283466880 z^3+450885600 z^4+224627904 z^5+31191840 z^6+764928 z^7
321111	21111111	2880+98400 z+1184640 z^2+6256800 z^3+14750880 z^4+14099520 z^5+4232640 z^6+199680 z^7	9600+2945280 z+65197440 z^2+314419200 z^3+445123200 z^4+194400000 z^5+22600320 z^6+399360 z^7
321111	111111111	1440+46800 z+529200 z^2+2574000 z^3+5401440 z^4+4286160 z^5+874800 z^6	12960+2635200 z+46418400 z^2+184291200 z^3+212565600 z^4+71375040 z^5+5248800 z^6
3111111	3111111	5040+187920 z+2511360 z^2+15089760 z^3+42038640 z^4+50687280 z^5+21939120 z^6+2198880 z^7+12960 z^8	1105920 z+48777120 z^2+371528640 z^3+783669600 z^4+518313600 z^5+101213280 z^6+4294080 z^7+12960 z^8
3111111	2211111	5040+177840 z+2226240 z^2+12348000 z^3+31051440 z^4+32533200 z^5+11334960 z^6+737280 z^7	7200+3245760 z+86819040 z^2+485251200 z^3+790725600 z^4+403704000 z^5+57687840 z^6+1474560 z^7
3111111	21111111	10080+354240 z+4413600 z^2+24343200 z^3+60792480 z^4+63120960 z^5+21712320 z^6+1382400 z^7	17280+7015680 z+180835200 z^2+987033600 z^3+1577923200 z^4+791320320 z^5+110920320 z^6+2764800 z^7
3111111	111111111	5040+166320 z+1915200 z^2+9525600 z^3+20568240 z^4+16969680 z^5+3674160 z^6	30240+7439040 z+144396000 z^2+617500800 z^3+762501600 z^4+275002560 z^5+22044960 z^6
22221	22221	2880+107376 z+1435752 z^2+8639736 z^3+24143304 z^4+29282976 z^5+12826080 z^6+1321920 z^7+8640 z^8	576+720000 z+28693440 z^2+212659200 z^3+445656960 z^4+296089344 z^5+58691520 z^6+2574720 z^7+8640 z^8
22221	222111	2880+103056 z+1311408 z^2+7418688 z^3+19120512 z^4+20693376 z^5+7554816 z^6+532224 z^7	2304+1428480 z+43068672 z^2+260697600 z^3+453934080 z^4+247021056 z^5+37877760 z^6+1064448 z^7
22221	2211111	2880+100656 z+1245528 z^2+6808968 z^3+16799832 z^4+17136576 z^5+5723136 z^6+342144 z^7	5184+2125440 z+53903232 z^2+288489600 z^3+450722880 z^4+219614976 z^5+29548800 z^6+684288 z^7
22221	21111111	2880+98976 z+1200672 z^2+6407616 z^3+15336384 z^4+15019776 z^5+4723200 z^6+253440 z^7	9216+2810880 z+62830080 z^2+307722240 z^3+445340160 z^4+201083904 z^5+24791040 z^6+506880 z^7
22221	111111111	2880+97680 z+1166760 z^2+6111480 z^3+14289000 z^4+13564800 z^5+4075200 z^6+201600 z^7	14400+3484800 z+70502400 z^2+322185600 z^3+439560000 z^4+187315200 z^5+21628800 z^6+403200 z^7
222111	222111	4320+158184 z+2070972 z^2+12150720 z^3+32901660 z^4+38289204 z^5+15807204 z^6+1475064 z^7+7560 z^8	2160+1575072 z+52837272 z^2+351097200 z^3+673417800 z^4+411410880 z^5+74404008 z^6+2889648 z^7+7560 z^8
222111	2211111	4320+152784 z+1917792 z^2+10672560 z^3+26951760 z^4+28399104 z^5+9978624 z^6+658944 z^7	5760+2679552 z+72824832 z^2+411874560 z^3+678268800 z^4+350023680 z^5+50646528 z^6+1317888 z^7
222111	21111111	4320+149760 z+1835640 z^2+9921600 z^3+24136920 z^4+24170040 z^5+7861320 z^6+449280 z^7	10800+3693600 z+87391440 z^2+446731200 z^3+672094800 z^4+315943200 z^5+40878000 z^6+898560 z^7
222111	111111111	4320+147600 z+1778400 z^2+9414000 z^3+22306320 z^4+21559680 z^5+6652800 z^6+345600 z^7	17280+4665600 z+99360000 z^2+471225600 z^3+664156800 z^4+292446720 z^5+35078400 z^6+691200 z^7
2211111	2211111	10080+366000 z+4744560 z^2+27506640 z^3+73375680 z^4+83712720 z^5+33578160 z^6+2981760 z^7+13440 z^8	7200+4320960 z+134853600 z^2+854098560 z^3+1573807200 z^4+924772800 z^5+160100640 z^6+5856000 z^7+13440 z^8
2211111	21111111	10080+354240 z+4413600 z^2+24343200 z^3+60792480 z^4+63120960 z^5+21712320 z^6+1382400 z^7	17280+7015680 z+180835200 z^2+987033600 z^3+1577923200 z^4+791320320 z^5+110920320 z^6+2764800 z^7
2211111	111111111	10080+347760 z+4238640 z^2+22755600 z^3+54895680 z^4+54366480 z^5+17403120 z^6+967680 z^7	30240+9374400 z+213222240 z^2+1061424000 z^3+1562047200 z^4+718925760 z^5+90871200 z^6+1935360 z^7
21111111	21111111	40320+1456560 z+18768960 z^2+108027360 z^3+285556320 z^4+321859440 z^5+126836640 z^6+10921680 z^7+45360 z^8	35280+19000800 z+568602720 z^2+3500511840 z^3+6297580800 z^4+3614677920 z^5+609386400 z^6+21480480 z^7+45360 z^8
21111111	111111111	40320+1411200 z+17498880 z^2+95961600 z^3+237928320 z^4+244702080 z^5+83018880 z^6+5160960 z^7	80640+30159360 z+752129280 z^2+4014259200 z^3+6297580800 z^4+3100930560 z^5+425859840 z^6+10321920 z^7
111111111	111111111	362880+13063680 z+167650560 z^2+960180480 z^3+2522378880 z^4+2819577600 z^5+1097712000 z^6+92534400 z^7+362880 z^8	362880+182165760 z+5300951040 z^2+32018353920 z^3+56678227200 z^4+32018353920 z^5+5300951040 z^6+182165760 z^7+362880 z^8