Implementation
const List<List<int>> correctionFactors = <List<int>>[
<int>[27, 917],
<int>[522, 568, 723, 809],
<int>[237, 308, 436, 284, 646, 653, 428, 379],
<int>[
274,
562,
232,
755,
599,
524,
801,
132,
295,
116,
442,
428,
295,
42,
176,
65,
],
<int>[
361,
575,
922,
525,
176,
586,
640,
321,
536,
742,
677,
742,
687,
284,
193,
517,
273,
494,
263,
147,
593,
800,
571,
320,
803,
133,
231,
390,
685,
330,
63,
410,
],
<int>[
539,
422,
6,
93,
862,
771,
453,
106,
610,
287,
107,
505,
733,
877,
381,
612,
723,
476,
462,
172,
430,
609,
858,
822,
543,
376,
511,
400,
672,
762,
283,
184,
440,
35,
519,
31,
460,
594,
225,
535,
517,
352,
605,
158,
651,
201,
488,
502,
648,
733,
717,
83,
404,
97,
280,
771,
840,
629,
4,
381,
843,
623,
264,
543,
],
<int>[
521,
310,
864,
547,
858,
580,
296,
379,
53,
779,
897,
444,
400,
925,
749,
415,
822,
93,
217,
208,
928,
244,
583,
620,
246,
148,
447,
631,
292,
908,
490,
704,
516,
258,
457,
907,
594,
723,
674,
292,
272,
96,
684,
432,
686,
606,
860,
569,
193,
219,
129,
186,
236,
287,
192,
775,
278,
173,
40,
379,
712,
463,
646,
776,
171,
491,
297,
763,
156,
732,
95,
270,
447,
90,
507,
48,
228,
821,
808,
898,
784,
663,
627,
378,
382,
262,
380,
602,
754,
336,
89,
614,
87,
432,
670,
616,
157,
374,
242,
726,
600,
269,
375,
898,
845,
454,
354,
130,
814,
587,
804,
34,
211,
330,
539,
297,
827,
865,
37,
517,
834,
315,
550,
86,
801,
4,
108,
539,
],
<int>[
524,
894,
75,
766,
882,
857,
74,
204,
82,
586,
708,
250,
905,
786,
138,
720,
858,
194,
311,
913,
275,
190,
375,
850,
438,
733,
194,
280,
201,
280,
828,
757,
710,
814,
919,
89,
68,
569,
11,
204,
796,
605,
540,
913,
801,
700,
799,
137,
439,
418,
592,
668,
353,
859,
370,
694,
325,
240,
216,
257,
284,
549,
209,
884,
315,
70,
329,
793,
490,
274,
877,
162,
749,
812,
684,
461,
334,
376,
849,
521,
307,
291,
803,
712,
19,
358,
399,
908,
103,
511,
51,
8,
517,
225,
289,
470,
637,
731,
66,
255,
917,
269,
463,
830,
730,
433,
848,
585,
136,
538,
906,
90,
2,
290,
743,
199,
655,
903,
329,
49,
802,
580,
355,
588,
188,
462,
10,
134,
628,
320,
479,
130,
739,
71,
263,
318,
374,
601,
192,
605,
142,
673,
687,
234,
722,
384,
177,
752,
607,
640,
455,
193,
689,
707,
805,
641,
48,
60,
732,
621,
895,
544,
261,
852,
655,
309,
697,
755,
756,
60,
231,
773,
434,
421,
726,
528,
503,
118,
49,
795,
32,
144,
500,
238,
836,
394,
280,
566,
319,
9,
647,
550,
73,
914,
342,
126,
32,
681,
331,
792,
620,
60,
609,
441,
180,
791,
893,
754,
605,
383,
228,
749,
760,
213,
54,
297,
134,
54,
834,
299,
922,
191,
910,
532,
609,
829,
189,
20,
167,
29,
872,
449,
83,
402,
41,
656,
505,
579,
481,
173,
404,
251,
688,
95,
497,
555,
642,
543,
307,
159,
924,
558,
648,
55,
497,
10,
],
<int>[
352,
77,
373,
504,
35,
599,
428,
207,
409,
574,
118,
498,
285,
380,
350,
492,
197,
265,
920,
155,
914,
299,
229,
643,
294,
871,
306,
88,
87,
193,
352,
781,
846,
75,
327,
520,
435,
543,
203,
666,
249,
346,
781,
621,
640,
268,
794,
534,
539,
781,
408,
390,
644,
102,
476,
499,
290,
632,
545,
37,
858,
916,
552,
41,
542,
289,
122,
272,
383,
800,
485,
98,
752,
472,
761,
107,
784,
860,
658,
741,
290,
204,
681,
407,
855,
85,
99,
62,
482,
180,
20,
297,
451,
593,
913,
142,
808,
684,
287,
536,
561,
76,
653,
899,
729,
567,
744,
390,
513,
192,
516,
258,
240,
518,
794,
395,
768,
848,
51,
610,
384,
168,
190,
826,
328,
596,
786,
303,
570,
381,
415,
641,
156,
237,
151,
429,
531,
207,
676,
710,
89,
168,
304,
402,
40,
708,
575,
162,
864,
229,
65,
861,
841,
512,
164,
477,
221,
92,
358,
785,
288,
357,
850,
836,
827,
736,
707,
94,
8,
494,
114,
521,
2,
499,
851,
543,
152,
729,
771,
95,
248,
361,
578,
323,
856,
797,
289,
51,
684,
466,
533,
820,
669,
45,
902,
452,
167,
342,
244,
173,
35,
463,
651,
51,
699,
591,
452,
578,
37,
124,
298,
332,
552,
43,
427,
119,
662,
777,
475,
850,
764,
364,
578,
911,
283,
711,
472,
420,
245,
288,
594,
394,
511,
327,
589,
777,
699,
688,
43,
408,
842,
383,
721,
521,
560,
644,
714,
559,
62,
145,
873,
663,
713,
159,
672,
729,
624,
59,
193,
417,
158,
209,
563,
564,
343,
693,
109,
608,
563,
365,
181,
772,
677,
310,
248,
353,
708,
410,
579,
870,
617,
841,
632,
860,
289,
536,
35,
777,
618,
586,
424,
833,
77,
597,
346,
269,
757,
632,
695,
751,
331,
247,
184,
45,
787,
680,
18,
66,
407,
369,
54,
492,
228,
613,
830,
922,
437,
519,
644,
905,
789,
420,
305,
441,
207,
300,
892,
827,
141,
537,
381,
662,
513,
56,
252,
341,
242,
797,
838,
837,
720,
224,
307,
631,
61,
87,
560,
310,
756,
665,
397,
808,
851,
309,
473,
795,
378,
31,
647,
915,
459,
806,
590,
731,
425,
216,
548,
249,
321,
881,
699,
535,
673,
782,
210,
815,
905,
303,
843,
922,
281,
73,
469,
791,
660,
162,
498,
308,
155,
422,
907,
817,
187,
62,
16,
425,
535,
336,
286,
437,
375,
273,
610,
296,
183,
923,
116,
667,
751,
353,
62,
366,
691,
379,
687,
842,
37,
357,
720,
742,
330,
5,
39,
923,
311,
424,
242,
749,
321,
54,
669,
316,
342,
299,
534,
105,
667,
488,
640,
672,
576,
540,
316,
486,
721,
610,
46,
656,
447,
171,
616,
464,
190,
531,
297,
321,
762,
752,
533,
175,
134,
14,
381,
433,
717,
45,
111,
20,
596,
284,
736,
138,
646,
411,
877,
669,
141,
919,
45,
780,
407,
164,
332,
899,
165,
726,
600,
325,
498,
655,
357,
752,
768,
223,
849,
647,
63,
310,
863,
251,
366,
304,
282,
738,
675,
410,
389,
244,
31,
121,
303,
263,
],
];
