Identifier
- St001361: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[1,0]=>2
[1,0,1,0]=>6
[1,1,0,0]=>4
[1,0,1,0,1,0]=>20
[1,0,1,1,0,0]=>16
[1,1,0,0,1,0]=>14
[1,1,0,1,0,0]=>12
[1,1,1,0,0,0]=>8
[1,0,1,0,1,0,1,0]=>70
[1,0,1,0,1,1,0,0]=>60
[1,0,1,1,0,0,1,0]=>58
[1,0,1,1,0,1,0,0]=>52
[1,0,1,1,1,0,0,0]=>40
[1,1,0,0,1,0,1,0]=>50
[1,1,0,0,1,1,0,0]=>44
[1,1,0,1,0,0,1,0]=>44
[1,1,0,1,0,1,0,0]=>40
[1,1,0,1,1,0,0,0]=>32
[1,1,1,0,0,0,1,0]=>30
[1,1,1,0,0,1,0,0]=>28
[1,1,1,0,1,0,0,0]=>24
[1,1,1,1,0,0,0,0]=>16
[1,0,1,0,1,0,1,0,1,0]=>252
[1,0,1,0,1,0,1,1,0,0]=>224
[1,0,1,0,1,1,0,0,1,0]=>222
[1,0,1,0,1,1,0,1,0,0]=>204
[1,0,1,0,1,1,1,0,0,0]=>168
[1,0,1,1,0,0,1,0,1,0]=>212
[1,0,1,1,0,0,1,1,0,0]=>192
[1,0,1,1,0,1,0,0,1,0]=>194
[1,0,1,1,0,1,0,1,0,0]=>180
[1,0,1,1,0,1,1,0,0,0]=>152
[1,0,1,1,1,0,0,0,1,0]=>152
[1,0,1,1,1,0,0,1,0,0]=>144
[1,0,1,1,1,0,1,0,0,0]=>128
[1,0,1,1,1,1,0,0,0,0]=>96
[1,1,0,0,1,0,1,0,1,0]=>182
[1,1,0,0,1,0,1,1,0,0]=>164
[1,1,0,0,1,1,0,0,1,0]=>164
[1,1,0,0,1,1,0,1,0,0]=>152
[1,1,0,0,1,1,1,0,0,0]=>128
[1,1,0,1,0,0,1,0,1,0]=>162
[1,1,0,1,0,0,1,1,0,0]=>148
[1,1,0,1,0,1,0,0,1,0]=>150
[1,1,0,1,0,1,0,1,0,0]=>140
[1,1,0,1,0,1,1,0,0,0]=>120
[1,1,0,1,1,0,0,0,1,0]=>122
[1,1,0,1,1,0,0,1,0,0]=>116
[1,1,0,1,1,0,1,0,0,0]=>104
[1,1,0,1,1,1,0,0,0,0]=>80
[1,1,1,0,0,0,1,0,1,0]=>112
[1,1,1,0,0,0,1,1,0,0]=>104
[1,1,1,0,0,1,0,0,1,0]=>106
[1,1,1,0,0,1,0,1,0,0]=>100
[1,1,1,0,0,1,1,0,0,0]=>88
[1,1,1,0,1,0,0,0,1,0]=>92
[1,1,1,0,1,0,0,1,0,0]=>88
[1,1,1,0,1,0,1,0,0,0]=>80
[1,1,1,0,1,1,0,0,0,0]=>64
[1,1,1,1,0,0,0,0,1,0]=>62
[1,1,1,1,0,0,0,1,0,0]=>60
[1,1,1,1,0,0,1,0,0,0]=>56
[1,1,1,1,0,1,0,0,0,0]=>48
[1,1,1,1,1,0,0,0,0,0]=>32
[1,0,1,0,1,0,1,0,1,0,1,0]=>924
[1,0,1,0,1,0,1,0,1,1,0,0]=>840
[1,0,1,0,1,0,1,1,0,0,1,0]=>840
[1,0,1,0,1,0,1,1,0,1,0,0]=>784
[1,0,1,0,1,0,1,1,1,0,0,0]=>672
[1,0,1,0,1,1,0,0,1,0,1,0]=>824
[1,0,1,0,1,1,0,0,1,1,0,0]=>760
[1,0,1,0,1,1,0,1,0,0,1,0]=>770
[1,0,1,0,1,1,0,1,0,1,0,0]=>724
[1,0,1,0,1,1,0,1,1,0,0,0]=>632
[1,0,1,0,1,1,1,0,0,0,1,0]=>644
[1,0,1,0,1,1,1,0,0,1,0,0]=>616
[1,0,1,0,1,1,1,0,1,0,0,0]=>560
[1,0,1,0,1,1,1,1,0,0,0,0]=>448
[1,0,1,1,0,0,1,0,1,0,1,0]=>784
[1,0,1,1,0,0,1,0,1,1,0,0]=>720
[1,0,1,1,0,0,1,1,0,0,1,0]=>724
[1,0,1,1,0,0,1,1,0,1,0,0]=>680
[1,0,1,1,0,0,1,1,1,0,0,0]=>592
[1,0,1,1,0,1,0,0,1,0,1,0]=>724
[1,0,1,1,0,1,0,0,1,1,0,0]=>672
[1,0,1,1,0,1,0,1,0,0,1,0]=>682
[1,0,1,1,0,1,0,1,0,1,0,0]=>644
[1,0,1,1,0,1,0,1,1,0,0,0]=>568
[1,0,1,1,0,1,1,0,0,0,1,0]=>584
[1,0,1,1,0,1,1,0,0,1,0,0]=>560
[1,0,1,1,0,1,1,0,1,0,0,0]=>512
[1,0,1,1,0,1,1,1,0,0,0,0]=>416
[1,0,1,1,1,0,0,0,1,0,1,0]=>574
[1,0,1,1,1,0,0,0,1,1,0,0]=>540
[1,0,1,1,1,0,0,1,0,0,1,0]=>550
[1,0,1,1,1,0,0,1,0,1,0,0]=>524
[1,0,1,1,1,0,0,1,1,0,0,0]=>472
[1,0,1,1,1,0,1,0,0,0,1,0]=>494
[1,0,1,1,1,0,1,0,0,1,0,0]=>476
[1,0,1,1,1,0,1,0,1,0,0,0]=>440
[1,0,1,1,1,0,1,1,0,0,0,0]=>368
[1,0,1,1,1,1,0,0,0,0,1,0]=>374
[1,0,1,1,1,1,0,0,0,1,0,0]=>364
[1,0,1,1,1,1,0,0,1,0,0,0]=>344
[1,0,1,1,1,1,0,1,0,0,0,0]=>304
[1,0,1,1,1,1,1,0,0,0,0,0]=>224
[1,1,0,0,1,0,1,0,1,0,1,0]=>672
[1,1,0,0,1,0,1,0,1,1,0,0]=>616
[1,1,0,0,1,0,1,1,0,0,1,0]=>618
[1,1,0,0,1,0,1,1,0,1,0,0]=>580
[1,1,0,0,1,0,1,1,1,0,0,0]=>504
[1,1,0,0,1,1,0,0,1,0,1,0]=>612
[1,1,0,0,1,1,0,0,1,1,0,0]=>568
[1,1,0,0,1,1,0,1,0,0,1,0]=>576
[1,1,0,0,1,1,0,1,0,1,0,0]=>544
[1,1,0,0,1,1,0,1,1,0,0,0]=>480
[1,1,0,0,1,1,1,0,0,0,1,0]=>492
[1,1,0,0,1,1,1,0,0,1,0,0]=>472
[1,1,0,0,1,1,1,0,1,0,0,0]=>432
[1,1,0,0,1,1,1,1,0,0,0,0]=>352
[1,1,0,1,0,0,1,0,1,0,1,0]=>602
[1,1,0,1,0,0,1,0,1,1,0,0]=>556
[1,1,0,1,0,0,1,1,0,0,1,0]=>560
[1,1,0,1,0,0,1,1,0,1,0,0]=>528
[1,1,0,1,0,0,1,1,1,0,0,0]=>464
[1,1,0,1,0,1,0,0,1,0,1,0]=>562
[1,1,0,1,0,1,0,0,1,1,0,0]=>524
[1,1,0,1,0,1,0,1,0,0,1,0]=>532
[1,1,0,1,0,1,0,1,0,1,0,0]=>504
[1,1,0,1,0,1,0,1,1,0,0,0]=>448
[1,1,0,1,0,1,1,0,0,0,1,0]=>462
[1,1,0,1,0,1,1,0,0,1,0,0]=>444
[1,1,0,1,0,1,1,0,1,0,0,0]=>408
[1,1,0,1,0,1,1,1,0,0,0,0]=>336
[1,1,0,1,1,0,0,0,1,0,1,0]=>462
[1,1,0,1,1,0,0,0,1,1,0,0]=>436
[1,1,0,1,1,0,0,1,0,0,1,0]=>444
[1,1,0,1,1,0,0,1,0,1,0,0]=>424
[1,1,0,1,1,0,0,1,1,0,0,0]=>384
[1,1,0,1,1,0,1,0,0,0,1,0]=>402
[1,1,0,1,1,0,1,0,0,1,0,0]=>388
[1,1,0,1,1,0,1,0,1,0,0,0]=>360
[1,1,0,1,1,0,1,1,0,0,0,0]=>304
[1,1,0,1,1,1,0,0,0,0,1,0]=>312
[1,1,0,1,1,1,0,0,0,1,0,0]=>304
[1,1,0,1,1,1,0,0,1,0,0,0]=>288
[1,1,0,1,1,1,0,1,0,0,0,0]=>256
[1,1,0,1,1,1,1,0,0,0,0,0]=>192
[1,1,1,0,0,0,1,0,1,0,1,0]=>420
[1,1,1,0,0,0,1,0,1,1,0,0]=>392
[1,1,1,0,0,0,1,1,0,0,1,0]=>396
[1,1,1,0,0,0,1,1,0,1,0,0]=>376
[1,1,1,0,0,0,1,1,1,0,0,0]=>336
[1,1,1,0,0,1,0,0,1,0,1,0]=>400
[1,1,1,0,0,1,0,0,1,1,0,0]=>376
[1,1,1,0,0,1,0,1,0,0,1,0]=>382
[1,1,1,0,0,1,0,1,0,1,0,0]=>364
[1,1,1,0,0,1,0,1,1,0,0,0]=>328
[1,1,1,0,0,1,1,0,0,0,1,0]=>340
[1,1,1,0,0,1,1,0,0,1,0,0]=>328
[1,1,1,0,0,1,1,0,1,0,0,0]=>304
[1,1,1,0,0,1,1,1,0,0,0,0]=>256
[1,1,1,0,1,0,0,0,1,0,1,0]=>350
[1,1,1,0,1,0,0,0,1,1,0,0]=>332
[1,1,1,0,1,0,0,1,0,0,1,0]=>338
[1,1,1,0,1,0,0,1,0,1,0,0]=>324
[1,1,1,0,1,0,0,1,1,0,0,0]=>296
[1,1,1,0,1,0,1,0,0,0,1,0]=>310
[1,1,1,0,1,0,1,0,0,1,0,0]=>300
[1,1,1,0,1,0,1,0,1,0,0,0]=>280
[1,1,1,0,1,0,1,1,0,0,0,0]=>240
[1,1,1,0,1,1,0,0,0,0,1,0]=>250
[1,1,1,0,1,1,0,0,0,1,0,0]=>244
[1,1,1,0,1,1,0,0,1,0,0,0]=>232
[1,1,1,0,1,1,0,1,0,0,0,0]=>208
[1,1,1,0,1,1,1,0,0,0,0,0]=>160
[1,1,1,1,0,0,0,0,1,0,1,0]=>238
[1,1,1,1,0,0,0,0,1,1,0,0]=>228
[1,1,1,1,0,0,0,1,0,0,1,0]=>232
[1,1,1,1,0,0,0,1,0,1,0,0]=>224
[1,1,1,1,0,0,0,1,1,0,0,0]=>208
[1,1,1,1,0,0,1,0,0,0,1,0]=>218
[1,1,1,1,0,0,1,0,0,1,0,0]=>212
[1,1,1,1,0,0,1,0,1,0,0,0]=>200
[1,1,1,1,0,0,1,1,0,0,0,0]=>176
[1,1,1,1,0,1,0,0,0,0,1,0]=>188
[1,1,1,1,0,1,0,0,0,1,0,0]=>184
[1,1,1,1,0,1,0,0,1,0,0,0]=>176
[1,1,1,1,0,1,0,1,0,0,0,0]=>160
[1,1,1,1,0,1,1,0,0,0,0,0]=>128
[1,1,1,1,1,0,0,0,0,0,1,0]=>126
[1,1,1,1,1,0,0,0,0,1,0,0]=>124
[1,1,1,1,1,0,0,0,1,0,0,0]=>120
[1,1,1,1,1,0,0,1,0,0,0,0]=>112
[1,1,1,1,1,0,1,0,0,0,0,0]=>96
[1,1,1,1,1,1,0,0,0,0,0,0]=>64
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>3432
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>3168
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>3180
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>3000
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2640
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>3152
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2944
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>2984
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>2832
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2528
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>2592
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2496
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2304
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>1920
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>3082
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>2868
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>2890
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>2740
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>2440
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>2902
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>2724
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>2764
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>2632
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2368
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>2442
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2356
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2184
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>1840
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>2452
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>2328
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>2368
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>2272
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>2080
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>2172
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2104
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>1968
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>1696
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>1752
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>1712
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>1632
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>1472
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>1152
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>2928
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>2720
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>2736
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2592
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>2304
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>2728
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>2560
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2596
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>2472
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>2224
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>2288
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>2208
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>2048
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>1728
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>2718
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2540
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2562
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2436
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>2184
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>2578
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2428
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>2464
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>2352
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2128
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>2198
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2124
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>1976
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>1680
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>2228
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>2120
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2156
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2072
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>1904
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>1988
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>1928
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>1808
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>1568
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>1628
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>1592
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>1520
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>1376
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>1088
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>2172
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>2048
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>2070
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>1980
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>1800
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>2092
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>1984
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2014
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>1932
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>1768
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>1832
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>1776
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>1664
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>1440
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>1892
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>1808
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>1838
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>1772
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>1640
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>1712
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>1664
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>1568
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>1376
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>1442
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>1412
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>1352
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>1232
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>992
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>1444
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>1392
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>1414
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>1372
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>1288
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>1344
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>1312
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>1248
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>1120
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>1194
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>1172
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>1128
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>1040
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>864
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>884
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>872
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>848
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>800
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>704
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>512
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>2508
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2328
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2340
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2216
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>1968
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2328
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>2184
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2214
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2108
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>1896
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>1948
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>1880
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>1744
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>1472
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2298
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>2148
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>2166
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>2060
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>1848
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2178
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>2052
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2082
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>1988
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>1800
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>1858
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>1796
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>1672
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>1424
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>1878
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>1788
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>1818
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>1748
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>1608
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>1678
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>1628
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>1528
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>1328
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>1378
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>1348
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>1288
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>1168
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>928
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>2256
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2104
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>2118
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2012
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>1800
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>2116
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>1992
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2020
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>1928
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>1744
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>1796
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>1736
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>1616
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>1376
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>2116
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>1984
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>2002
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>1908
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>1720
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>2016
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>1904
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1932
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1848
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>1680
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>1736
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>1680
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>1568
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>1344
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>1766
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>1684
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>1712
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>1648
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>1520
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>1586
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>1540
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>1448
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>1264
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>1316
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>1288
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>1232
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>1120
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>896
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>1752
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>1656
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>1674
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>1604
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>1464
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>1692
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>1608
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>1632
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>1568
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>1440
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>1492
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>1448
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>1360
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>1184
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>1542
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>1476
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>1500
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>1448
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>1344
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>1402
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>1364
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>1288
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>1136
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>1192
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>1168
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>1120
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>1024
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>832
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>1206
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>1164
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>1182
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>1148
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>1080
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>1126
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>1100
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>1048
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>944
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>1006
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>988
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>952
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>880
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>736
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>758
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>748
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>728
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>688
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>608
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>448
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>1584
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>1488
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>1500
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>1432
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>1296
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>1504
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>1424
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>1444
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>1384
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>1264
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>1304
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>1264
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>1184
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>1024
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>1514
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>1428
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>1442
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>1380
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>1256
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>1454
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>1380
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>1400
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>1344
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>1232
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>1274
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>1236
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>1160
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>1008
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>1304
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>1248
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>1268
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>1224
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>1136
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>1184
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>1152
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>1088
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>960
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>1004
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>984
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>944
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>864
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>704
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>1332
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>1264
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>1278
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>1228
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>1128
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>1292
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>1232
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>1250
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>1204
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>1112
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>1152
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>1120
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>1056
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>928
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>1192
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>1144
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>1162
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>1124
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>1048
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>1092
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>1064
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>1008
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>896
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>942
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>924
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>888
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>816
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>672
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>968
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>936
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>950
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>924
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>872
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>908
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>888
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>848
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>768
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>818
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>804
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>776
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>720
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>608
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>632
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>624
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>608
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>576
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>512
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>384
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>912
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>872
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>882
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>852
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>792
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>892
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>856
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>868
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>840
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>784
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>812
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>792
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>752
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>672
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>842
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>812
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>824
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>800
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>752
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>782
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>764
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>728
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>656
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>692
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>680
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>656
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>608
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>512
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>730
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>708
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>718
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>700
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>664
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>690
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>676
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>648
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>592
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>630
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>620
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>600
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>560
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>480
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>506
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>500
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>488
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>464
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>416
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>320
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>492
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>480
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>486
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>476
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>456
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>472
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>464
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>448
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>416
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>442
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>436
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>424
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>400
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>352
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>380
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>376
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>368
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>352
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>320
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>256
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>254
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>252
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>248
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>240
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>224
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>192
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>128
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>12870
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>12012
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>12078
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>11484
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>10296
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>12030
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>11340
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>11490
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>10980
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>9960
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>10230
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>9900
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>9240
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>7920
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>11890
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>11172
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>11266
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>10756
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>9736
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>11330
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>10724
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>10874
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>10420
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>9512
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>9810
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>9508
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>8904
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>7696
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>9930
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>9492
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>9642
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>9300
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>8616
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>8970
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>8724
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>8232
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>7248
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>7530
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>7380
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>7080
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>6480
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>5280
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>11610
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>10892
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>10968
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>10464
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>9456
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>10970
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>10380
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>10520
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>10080
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>9200
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>9470
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>9180
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>8600
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>7440
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>10980
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>10352
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>10446
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>9996
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>9096
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>10520
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>9984
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>10124
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>9720
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>8912
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>9200
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>8928
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>8384
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>7296
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>9370
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>8972
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>9112
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>8800
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>8176
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>8510
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>8284
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>7832
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>6928
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>7220
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>7080
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>6800
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>6240
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>5120
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>9342
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>8876
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>8970
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>8628
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>7944
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>9062
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>8652
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>8774
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>8460
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>7832
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>8102
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>7884
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>7448
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>6576
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>8362
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>8036
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>8158
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>7900
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>7384
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>7682
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>7492
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>7112
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>6352
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>6662
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>6540
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>6296
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>5808
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>4832
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>6794
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>6580
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>6674
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>6500
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>6152
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>6394
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>6260
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>5992
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>5456
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>5794
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>5700
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>5512
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>5136
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>4384
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>4554
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>4500
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>4392
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>4176
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>3744
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>2880
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>11022
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>10332
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>10398
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>9916
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>8952
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>10382
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>9820
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>9950
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>9532
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>8696
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>8942
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>8668
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>8120
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>7024
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>10322
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>9732
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>9818
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>9396
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>8552
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>9882
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>9380
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>9510
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>9132
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>8376
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>8642
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>8388
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>7880
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>6864
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>8782
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>8412
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>8542
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>8252
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>7672
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>7982
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>7772
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>7352
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>6512
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>6782
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>6652
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>6392
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>5872
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>4832
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>10266
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>9660
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>9732
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>9304
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>8448
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>9746
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>9244
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>9368
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>8992
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>8240
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>8486
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>8236
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>7736
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>6736
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>9776
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>9240
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>9326
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>8940
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>8168
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>9396
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>8936
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>9060
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>8712
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>8016
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>8276
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>8040
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>7568
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>6624
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>8446
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>8100
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>8224
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>7952
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>7408
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>7706
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>7508
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>7112
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>6320
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>6596
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>6472
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>6224
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>5728
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>4736
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>8502
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>8092
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>8178
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>7876
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>7272
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>8262
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>7900
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>8010
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>7732
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>7176
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>7422
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>7228
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>6840
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>6064
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>7662
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>7372
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>7482
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>7252
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>6792
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>7062
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>6892
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>6552
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>5872
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>6162
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>6052
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>5832
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>5392
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>4512
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>6318
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>6124
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>6210
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>6052
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>5736
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>5958
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>5836
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>5592
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>5104
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>5418
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>5332
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>5160
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>4816
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>4128
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>4302
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>4252
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>4152
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>3952
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>3552
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>2752
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>8250
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>7812
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>7878
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>7564
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>6936
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>7910
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>7540
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>7640
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>7360
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>6800
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>7010
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>6820
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>6440
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>5680
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>7970
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>7572
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>7646
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>7356
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>6776
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>7710
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>7364
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>7464
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>7200
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>6672
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>6890
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>6708
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>6344
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>5616
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>7060
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>6792
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>6892
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>6680
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>6256
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>6500
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>6344
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>6032
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>5408
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>5660
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>5560
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>5360
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>4960
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>4160
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>7242
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>6916
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>6990
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>6748
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>6264
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>7062
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>6772
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>6864
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>6640
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>6192
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>6402
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>6244
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>5928
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>5296
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>6612
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>6376
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>6468
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>6280
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>5904
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>6132
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>5992
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>5712
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>5152
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>5412
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>5320
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>5136
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>4768
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>4032
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>5604
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>5440
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>5514
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>5380
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>5112
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>5304
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>5200
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>4992
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>4576
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>4854
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>4780
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>4632
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>4336
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>3744
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>3924
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>3880
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>3792
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>3616
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>3264
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>2560
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>5562
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>5348
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>5406
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>5244
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>4920
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>5462
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>5268
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>5336
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>5184
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>4880
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>5042
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>4932
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>4712
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>4272
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>5212
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>5048
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>5116
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>4984
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>4720
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>4892
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>4792
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>4592
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>4192
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>4412
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>4344
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>4208
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>3936
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>3392
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>4652
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>4528
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>4586
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>4484
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>4280
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>4432
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>4352
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>4192
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>3872
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>4102
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>4044
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>3928
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>3696
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>3232
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>3420
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>3384
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>3312
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>3168
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>2880
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>2304
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>3462
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>3388
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>3426
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>3364
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>3240
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>3342
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>3292
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>3192
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>2992
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>3162
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>3124
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>3048
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>2896
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>2592
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>2790
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>2764
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>2712
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>2608
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>2400
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>1984
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>2034
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>2020
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>1992
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>1936
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>1824
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>1600
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>1152
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>9438
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>8844
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8898
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>8484
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>7656
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8878
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>8396
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>8506
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>8148
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>7432
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>7638
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>7404
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>6936
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>6000
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8808
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>8304
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>8376
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>8016
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>7296
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>8428
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>8000
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>8110
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>7788
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>7144
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>7368
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>7152
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>6720
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>5856
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>7478
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>7164
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>7274
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>7028
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>6536
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>6798
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>6620
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>6264
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>5552
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>5778
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>5668
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>5448
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>5008
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>4128
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8682
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>8172
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>8232
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>7872
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>7152
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>8242
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>7820
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>7924
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>7608
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>6976
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>7182
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>6972
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>6552
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>5712
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>8262
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>7812
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>7884
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>7560
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>6912
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>7942
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>7556
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>7660
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>7368
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>6784
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>7002
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>6804
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>6408
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>5616
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>7142
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>6852
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>6956
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>6728
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>6272
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>6522
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>6356
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>6024
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>5360
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>5592
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>5488
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>5280
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>4864
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>4032
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>7170
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>6828
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>6900
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>6648
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>6144
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>6970
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>6668
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>6760
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>6528
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>6064
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>6270
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>6108
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>5784
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>5136
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>6470
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>6228
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>6320
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>6128
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>5744
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>5970
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>5828
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>5544
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>4976
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>5220
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>5128
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>4944
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>4576
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>3840
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>5350
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>5188
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>5260
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>5128
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>4864
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>5050
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>4948
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>4744
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>4336
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>4600
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>4528
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>4384
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>4096
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>3520
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>3670
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>3628
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>3544
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>3376
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>3040
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>2368
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>8514
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>8004
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>8058
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>7700
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>6984
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>8054
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>7636
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>7736
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>7424
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>6800
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>6994
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>6788
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>6376
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>5552
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Description
The number of lattice paths of the same length that stay weakly above a Dyck path.
In particular, the statistic value is $2^n$ for the Dyck path consisting of $n$ north steps followed by $n$ east steps and the central binomial coefficient $\binom{2n}{n}$ for the Dyck path consisting of $n$ alternating north and east steps.
The number of such paths is always even: the final step of a Dyck path $D$ must be a down step. Thus, the final step of a path above $D$ can be arbitrarily chosen.
In particular, the statistic value is $2^n$ for the Dyck path consisting of $n$ north steps followed by $n$ east steps and the central binomial coefficient $\binom{2n}{n}$ for the Dyck path consisting of $n$ alternating north and east steps.
The number of such paths is always even: the final step of a Dyck path $D$ must be a down step. Thus, the final step of a path above $D$ can be arbitrarily chosen.
Code
@cached_function def all_paths_above(L, i=0): if i < 0: return [] elif len(L) == 0: return [tuple()] else: steps = [] if L[0] == 1: steps.append((1,i)) steps.append((0,i-1)) if L[0] == 0: steps.append((1,i+1)) steps.append((0,i)) return [ tuple([a]) + path for a,i in steps for path in all_paths_above(L[1:],i)] def statistic(D): return len(all_paths_above(tuple(D)))
Created
Mar 04, 2019 at 14:56 by Christian Stump
Updated
Mar 10, 2019 at 08:02 by Martin Rubey
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