#include <bits/stdc++.h>   using namespace std;   template <typename T, typename U>   std::istream& operator>>(std::istream& i, pair<T, U>& p) {     i >> p.first >> p.second;     return i;   }   template <typename T>   std::istream& operator>>(std::istream& i, vector<T>& t) {     for (auto& v : t) {       i >> v;     }     return i;   }   template <typename T, typename U>   std::ostream& operator<<(std::ostream& o, const pair<T, U>& p) {     o << p.first <<     << p.second;     return o;   }   template <typename T>   std::ostream& operator<<(std::ostream& o, const vector<T>& t) {     if (t.empty()) o <<   n ;     for (size_t i = 0; i < t.size(); ++i) {       o << t[i] <<    n [i == t.size() - 1];     }     return o;   }   template <typename T>   using minheap = priority_queue<T, vector<T>, greater<T>>;   template <typename T>   using maxheap = priority_queue<T, vector<T>, less<T>>;   template <typename T>   bool in(T a, T b, T c) {     return a <= b && b < c;   }   unsigned int logceil(int first) {     return first ? 8 * sizeof(int) - __builtin_clz(first) : 0;   }   namespace std {   template <typename T, typename U>   struct hash<pair<T, U>> {     hash<T> t;     hash<U> u;     size_t operator()(const pair<T, U>& p) const {       return t(p.first) ^ (u(p.second) << 7);     }   };   }  // namespace std   template <typename T, typename F>   T bsh(T l, T h, const F& f) {     T r = -1, m;     while (l <= h) {       m = (l + h) / 2;       if (f(m)) {         l = m + 1;         r = m;       } else {         h = m - 1;       }     }     return r;   }   template <typename F>   double bshd(double l, double h, const F& f, double p = 1e-9) {     unsigned int r = 3 + (unsigned int)log2((h - l) / p);     while (r--) {       double m = (l + h) / 2;       if (f(m)) {         l = m;       } else {         h = m;       }     }     return (l + h) / 2;   }   template <typename T, typename F>   T bsl(T l, T h, const F& f) {     T r = -1, m;     while (l <= h) {       m = (l + h) / 2;       if (f(m)) {         h = m - 1;         r = m;       } else {         l = m + 1;       }     }     return r;   }   template <typename F>   double bsld(double l, double h, const F& f, double p = 1e-9) {     unsigned int r = 3 + (unsigned int)log2((h - l) / p);     while (r--) {       double m = (l + h) / 2;       if (f(m)) {         h = m;       } else {         l = m;       }     }     return (l + h) / 2;   }   template <typename T>   T gcd(T a, T b) {     if (a < b) swap(a, b);     return b ? gcd(b, a % b) : a;   }   template <typename T>   class vector2 : public vector<vector<T>> {    public:     vector2() {}     vector2(size_t a, size_t b, T t = T())         : vector<vector<T>>(a, vector<T>(b, t)) {}   };   template <typename T>   class vector3 : public vector<vector2<T>> {    public:     vector3() {}     vector3(size_t a, size_t b, size_t c, T t = T())         : vector<vector2<T>>(a, vector2<T>(b, c, t)) {}   };   template <typename T>   class vector4 : public vector<vector3<T>> {    public:     vector4() {}     vector4(size_t a, size_t b, size_t c, size_t d, T t = T())         : vector<vector3<T>>(a, vector3<T>(b, c, d, t)) {}   };   template <typename T>   class vector5 : public vector<vector4<T>> {    public:     vector5() {}     vector5(size_t a, size_t b, size_t c, size_t d, size_t e, T t = T())         : vector<vector4<T>>(a, vector4<T>(b, c, d, e, t)) {}   };   class TaskD {    public:     vector<int> P;     void fact(int a, vector<int>& f) {       while (a != 1) {         int b = P[a], c = 0;         while (P[a] == b) {           c++;           a /= b;         }         f.push_back(c + 1);       }       sort(f.begin(), f.end());       reverse(f.begin(), f.end());       while (f.size() < Prm.size()) f.push_back(1);     }     vector<vector<int>> HH;     vector<int> Used, CNT;     map<vector<int>, int> J;     vector<int> X;     void genAll(int p, int m, int c, int d) {       if (p == Prm.size()) {         HH.push_back(X);         CNT.push_back(d);         int second = J.size();         if (c <= 1e6) Used.push_back(second);         J[X] = second;       } else {         X[p] = 1;         genAll(p + 1, 1, c, d * X[p]);         while (true) {           X[p]++;           c *= Prm[p];           if (c > 55050240) return;           if (X[p] > m) return;           genAll(p + 1, X[p], c, d * X[p]);         }       }     }     vector<int> Prm;     void solve(istream& cin, ostream& cout) {       Prm = {2, 3, 5, 7, 11, 13, 17};       P.assign(1e6 + 5, 0);       for (int i = 2; i < 1e6 + 3; ++i) {         if (P[i] == 0) {           for (int j = i; j < 1e6 + 3; j += i) P[j] = i;         }       }       map<vector<int>, int> IDX{           {{1, 1, 1, 1, 1, 1, 1}, 0},    {{2, 1, 1, 1, 1, 1, 1}, 1},           {{2, 2, 1, 1, 1, 1, 1}, 2},    {{2, 2, 2, 1, 1, 1, 1}, 3},           {{2, 2, 2, 2, 1, 1, 1}, 4},    {{2, 2, 2, 2, 2, 1, 1}, 5},           {{2, 2, 2, 2, 2, 2, 1}, 6},    {{2, 2, 2, 2, 2, 2, 2}, 7},           {{3, 1, 1, 1, 1, 1, 1}, 8},    {{3, 2, 1, 1, 1, 1, 1}, 9},           {{3, 2, 2, 1, 1, 1, 1}, 10},   {{3, 2, 2, 2, 1, 1, 1}, 11},           {{3, 2, 2, 2, 2, 1, 1}, 12},   {{3, 2, 2, 2, 2, 2, 1}, 13},           {{3, 3, 1, 1, 1, 1, 1}, 14},   {{3, 3, 2, 1, 1, 1, 1}, 15},           {{3, 3, 2, 2, 1, 1, 1}, 16},   {{3, 3, 2, 2, 2, 1, 1}, 17},           {{3, 3, 2, 2, 2, 2, 1}, 18},   {{3, 3, 3, 1, 1, 1, 1}, 19},           {{3, 3, 3, 2, 1, 1, 1}, 20},   {{3, 3, 3, 2, 2, 1, 1}, 21},           {{3, 3, 3, 2, 2, 2, 1}, 22},   {{3, 3, 3, 3, 1, 1, 1}, 23},           {{3, 3, 3, 3, 2, 1, 1}, 24},   {{4, 1, 1, 1, 1, 1, 1}, 25},           {{4, 2, 1, 1, 1, 1, 1}, 26},   {{4, 2, 2, 1, 1, 1, 1}, 27},           {{4, 2, 2, 2, 1, 1, 1}, 28},   {{4, 2, 2, 2, 2, 1, 1}, 29},           {{4, 2, 2, 2, 2, 2, 1}, 30},   {{4, 3, 1, 1, 1, 1, 1}, 31},           {{4, 3, 2, 1, 1, 1, 1}, 32},   {{4, 3, 2, 2, 1, 1, 1}, 33},           {{4, 3, 2, 2, 2, 1, 1}, 34},   {{4, 3, 2, 2, 2, 2, 1}, 35},           {{4, 3, 3, 1, 1, 1, 1}, 36},   {{4, 3, 3, 2, 1, 1, 1}, 37},           {{4, 3, 3, 2, 2, 1, 1}, 38},   {{4, 3, 3, 3, 1, 1, 1}, 39},           {{4, 3, 3, 3, 2, 1, 1}, 40},   {{4, 4, 1, 1, 1, 1, 1}, 41},           {{4, 4, 2, 1, 1, 1, 1}, 42},   {{4, 4, 2, 2, 1, 1, 1}, 43},           {{4, 4, 2, 2, 2, 1, 1}, 44},   {{4, 4, 3, 1, 1, 1, 1}, 45},           {{4, 4, 3, 2, 1, 1, 1}, 46},   {{4, 4, 3, 2, 2, 1, 1}, 47},           {{4, 4, 3, 3, 1, 1, 1}, 48},   {{4, 4, 4, 1, 1, 1, 1}, 49},           {{4, 4, 4, 2, 1, 1, 1}, 50},   {{5, 1, 1, 1, 1, 1, 1}, 51},           {{5, 2, 1, 1, 1, 1, 1}, 52},   {{5, 2, 2, 1, 1, 1, 1}, 53},           {{5, 2, 2, 2, 1, 1, 1}, 54},   {{5, 2, 2, 2, 2, 1, 1}, 55},           {{5, 2, 2, 2, 2, 2, 1}, 56},   {{5, 3, 1, 1, 1, 1, 1}, 57},           {{5, 3, 2, 1, 1, 1, 1}, 58},   {{5, 3, 2, 2, 1, 1, 1}, 59},           {{5, 3, 2, 2, 2, 1, 1}, 60},   {{5, 3, 2, 2, 2, 2, 1}, 61},           {{5, 3, 3, 1, 1, 1, 1}, 62},   {{5, 3, 3, 2, 1, 1, 1}, 63},           {{5, 3, 3, 2, 2, 1, 1}, 64},   {{5, 3, 3, 3, 1, 1, 1}, 65},           {{5, 4, 1, 1, 1, 1, 1}, 66},   {{5, 4, 2, 1, 1, 1, 1}, 67},           {{5, 4, 2, 2, 1, 1, 1}, 68},   {{5, 4, 2, 2, 2, 1, 1}, 69},           {{5, 4, 3, 1, 1, 1, 1}, 70},   {{5, 4, 3, 2, 1, 1, 1}, 71},           {{5, 4, 3, 2, 2, 1, 1}, 72},   {{5, 4, 3, 3, 1, 1, 1}, 73},           {{5, 4, 4, 1, 1, 1, 1}, 74},   {{5, 4, 4, 2, 1, 1, 1}, 75},           {{5, 5, 1, 1, 1, 1, 1}, 76},   {{5, 5, 2, 1, 1, 1, 1}, 77},           {{5, 5, 2, 2, 1, 1, 1}, 78},   {{5, 5, 2, 2, 2, 1, 1}, 79},           {{5, 5, 3, 1, 1, 1, 1}, 80},   {{5, 5, 3, 2, 1, 1, 1}, 81},           {{5, 5, 4, 1, 1, 1, 1}, 82},   {{5, 5, 5, 1, 1, 1, 1}, 83},           {{6, 1, 1, 1, 1, 1, 1}, 84},   {{6, 2, 1, 1, 1, 1, 1}, 85},           {{6, 2, 2, 1, 1, 1, 1}, 86},   {{6, 2, 2, 2, 1, 1, 1}, 87},           {{6, 2, 2, 2, 2, 1, 1}, 88},   {{6, 2, 2, 2, 2, 2, 1}, 89},           {{6, 3, 1, 1, 1, 1, 1}, 90},   {{6, 3, 2, 1, 1, 1, 1}, 91},           {{6, 3, 2, 2, 1, 1, 1}, 92},   {{6, 3, 2, 2, 2, 1, 1}, 93},           {{6, 3, 3, 1, 1, 1, 1}, 94},   {{6, 3, 3, 2, 1, 1, 1}, 95},           {{6, 3, 3, 2, 2, 1, 1}, 96},   {{6, 3, 3, 3, 1, 1, 1}, 97},           {{6, 4, 1, 1, 1, 1, 1}, 98},   {{6, 4, 2, 1, 1, 1, 1}, 99},           {{6, 4, 2, 2, 1, 1, 1}, 100},  {{6, 4, 2, 2, 2, 1, 1}, 101},           {{6, 4, 3, 1, 1, 1, 1}, 102},  {{6, 4, 3, 2, 1, 1, 1}, 103},           {{6, 4, 4, 1, 1, 1, 1}, 104},  {{6, 4, 4, 2, 1, 1, 1}, 105},           {{6, 5, 1, 1, 1, 1, 1}, 106},  {{6, 5, 2, 1, 1, 1, 1}, 107},           {{6, 5, 2, 2, 1, 1, 1}, 108},  {{6, 5, 2, 2, 2, 1, 1}, 109},           {{6, 5, 3, 1, 1, 1, 1}, 110},  {{6, 5, 3, 2, 1, 1, 1}, 111},           {{6, 5, 4, 1, 1, 1, 1}, 112},  {{6, 6, 1, 1, 1, 1, 1}, 113},           {{6, 6, 2, 1, 1, 1, 1}, 114},  {{6, 6, 2, 2, 1, 1, 1}, 115},           {{6, 6, 3, 1, 1, 1, 1}, 116},  {{6, 6, 4, 1, 1, 1, 1}, 117},           {{7, 1, 1, 1, 1, 1, 1}, 118},  {{7, 2, 1, 1, 1, 1, 1}, 119},           {{7, 2, 2, 1, 1, 1, 1}, 120},  {{7, 2, 2, 2, 1, 1, 1}, 121},           {{7, 2, 2, 2, 2, 1, 1}, 122},  {{7, 2, 2, 2, 2, 2, 1}, 123},           {{7, 3, 1, 1, 1, 1, 1}, 124},  {{7, 3, 2, 1, 1, 1, 1}, 125},           {{7, 3, 2, 2, 1, 1, 1}, 126},  {{7, 3, 2, 2, 2, 1, 1}, 127},           {{7, 3, 3, 1, 1, 1, 1}, 128},  {{7, 3, 3, 2, 1, 1, 1}, 129},           {{7, 3, 3, 3, 1, 1, 1}, 130},  {{7, 4, 1, 1, 1, 1, 1}, 131},           {{7, 4, 2, 1, 1, 1, 1}, 132},  {{7, 4, 2, 2, 1, 1, 1}, 133},           {{7, 4, 2, 2, 2, 1, 1}, 134},  {{7, 4, 3, 1, 1, 1, 1}, 135},           {{7, 4, 3, 2, 1, 1, 1}, 136},  {{7, 4, 4, 1, 1, 1, 1}, 137},           {{7, 5, 1, 1, 1, 1, 1}, 138},  {{7, 5, 2, 1, 1, 1, 1}, 139},           {{7, 5, 2, 2, 1, 1, 1}, 140},  {{7, 5, 3, 1, 1, 1, 1}, 141},           {{7, 5, 3, 2, 1, 1, 1}, 142},  {{7, 5, 4, 1, 1, 1, 1}, 143},           {{7, 6, 1, 1, 1, 1, 1}, 144},  {{7, 6, 2, 1, 1, 1, 1}, 145},           {{7, 6, 2, 2, 1, 1, 1}, 146},  {{7, 6, 3, 1, 1, 1, 1}, 147},           {{7, 7, 1, 1, 1, 1, 1}, 148},  {{7, 7, 2, 1, 1, 1, 1}, 149},           {{8, 1, 1, 1, 1, 1, 1}, 150},  {{8, 2, 1, 1, 1, 1, 1}, 151},           {{8, 2, 2, 1, 1, 1, 1}, 152},  {{8, 2, 2, 2, 1, 1, 1}, 153},           {{8, 2, 2, 2, 2, 1, 1}, 154},  {{8, 3, 1, 1, 1, 1, 1}, 155},           {{8, 3, 2, 1, 1, 1, 1}, 156},  {{8, 3, 2, 2, 1, 1, 1}, 157},           {{8, 3, 2, 2, 2, 1, 1}, 158},  {{8, 3, 3, 1, 1, 1, 1}, 159},           {{8, 3, 3, 2, 1, 1, 1}, 160},  {{8, 4, 1, 1, 1, 1, 1}, 161},           {{8, 4, 2, 1, 1, 1, 1}, 162},  {{8, 4, 2, 2, 1, 1, 1}, 163},           {{8, 4, 3, 1, 1, 1, 1}, 164},  {{8, 4, 3, 2, 1, 1, 1}, 165},           {{8, 4, 4, 1, 1, 1, 1}, 166},  {{8, 5, 1, 1, 1, 1, 1}, 167},           {{8, 5, 2, 1, 1, 1, 1}, 168},  {{8, 5, 2, 2, 1, 1, 1}, 169},           {{8, 5, 3, 1, 1, 1, 1}, 170},  {{8, 6, 1, 1, 1, 1, 1}, 171},           {{8, 6, 2, 1, 1, 1, 1}, 172},  {{8, 6, 3, 1, 1, 1, 1}, 173},           {{8, 7, 1, 1, 1, 1, 1}, 174},  {{8, 7, 2, 1, 1, 1, 1}, 175},           {{8, 8, 1, 1, 1, 1, 1}, 176},  {{9, 1, 1, 1, 1, 1, 1}, 177},           {{9, 2, 1, 1, 1, 1, 1}, 178},  {{9, 2, 2, 1, 1, 1, 1}, 179},           {{9, 2, 2, 2, 1, 1, 1}, 180},  {{9, 2, 2, 2, 2, 1, 1}, 181},           {{9, 3, 1, 1, 1, 1, 1}, 182},  {{9, 3, 2, 1, 1, 1, 1}, 183},           {{9, 3, 2, 2, 1, 1, 1}, 184},  {{9, 3, 2, 2, 2, 1, 1}, 185},           {{9, 3, 3, 1, 1, 1, 1}, 186},  {{9, 3, 3, 2, 1, 1, 1}, 187},           {{9, 4, 1, 1, 1, 1, 1}, 188},  {{9, 4, 2, 1, 1, 1, 1}, 189},           {{9, 4, 2, 2, 1, 1, 1}, 190},  {{9, 4, 3, 1, 1, 1, 1}, 191},           {{9, 4, 4, 1, 1, 1, 1}, 192},  {{9, 5, 1, 1, 1, 1, 1}, 193},           {{9, 5, 2, 1, 1, 1, 1}, 194},  {{9, 5, 2, 2, 1, 1, 1}, 195},           {{9, 5, 3, 1, 1, 1, 1}, 196},  {{9, 6, 1, 1, 1, 1, 1}, 197},           {{9, 6, 2, 1, 1, 1, 1}, 198},  {{9, 7, 1, 1, 1, 1, 1}, 199},           {{9, 7, 2, 1, 1, 1, 1}, 200},  {{9, 8, 1, 1, 1, 1, 1}, 201},           {{10, 1, 1, 1, 1, 1, 1}, 202}, {{10, 2, 1, 1, 1, 1, 1}, 203},           {{10, 2, 2, 1, 1, 1, 1}, 204}, {{10, 2, 2, 2, 1, 1, 1}, 205},           {{10, 2, 2, 2, 2, 1, 1}, 206}, {{10, 3, 1, 1, 1, 1, 1}, 207},           {{10, 3, 2, 1, 1, 1, 1}, 208}, {{10, 3, 2, 2, 1, 1, 1}, 209},           {{10, 3, 3, 1, 1, 1, 1}, 210}, {{10, 3, 3, 2, 1, 1, 1}, 211},           {{10, 4, 1, 1, 1, 1, 1}, 212}, {{10, 4, 2, 1, 1, 1, 1}, 213},           {{10, 4, 2, 2, 1, 1, 1}, 214}, {{10, 4, 3, 1, 1, 1, 1}, 215},           {{10, 5, 1, 1, 1, 1, 1}, 216}, {{10, 5, 2, 1, 1, 1, 1}, 217},           {{10, 6, 1, 1, 1, 1, 1}, 218}, {{10, 6, 2, 1, 1, 1, 1}, 219},           {{10, 7, 1, 1, 1, 1, 1}, 220}, {{11, 1, 1, 1, 1, 1, 1}, 221},           {{11, 2, 1, 1, 1, 1, 1}, 222}, {{11, 2, 2, 1, 1, 1, 1}, 223},           {{11, 2, 2, 2, 1, 1, 1}, 224}, {{11, 3, 1, 1, 1, 1, 1}, 225},           {{11, 3, 2, 1, 1, 1, 1}, 226}, {{11, 3, 2, 2, 1, 1, 1}, 227},           {{11, 3, 3, 1, 1, 1, 1}, 228}, {{11, 4, 1, 1, 1, 1, 1}, 229},           {{11, 4, 2, 1, 1, 1, 1}, 230}, {{11, 4, 2, 2, 1, 1, 1}, 231},           {{11, 4, 3, 1, 1, 1, 1}, 232}, {{11, 5, 1, 1, 1, 1, 1}, 233},           {{11, 5, 2, 1, 1, 1, 1}, 234}, {{11, 6, 1, 1, 1, 1, 1}, 235},           {{11, 7, 1, 1, 1, 1, 1}, 236}, {{12, 1, 1, 1, 1, 1, 1}, 237},           {{12, 2, 1, 1, 1, 1, 1}, 238}, {{12, 2, 2, 1, 1, 1, 1}, 239},           {{12, 2, 2, 2, 1, 1, 1}, 240}, {{12, 3, 1, 1, 1, 1, 1}, 241},           {{12, 3, 2, 1, 1, 1, 1}, 242}, {{12, 3, 2, 2, 1, 1, 1}, 243},           {{12, 3, 3, 1, 1, 1, 1}, 244}, {{12, 4, 1, 1, 1, 1, 1}, 245},           {{12, 4, 2, 1, 1, 1, 1}, 246}, {{12, 5, 1, 1, 1, 1, 1}, 247},           {{12, 5, 2, 1, 1, 1, 1}, 248}, {{12, 6, 1, 1, 1, 1, 1}, 249},           {{13, 1, 1, 1, 1, 1, 1}, 250}, {{13, 2, 1, 1, 1, 1, 1}, 251},           {{13, 2, 2, 1, 1, 1, 1}, 252}, {{13, 2, 2, 2, 1, 1, 1}, 253},           {{13, 3, 1, 1, 1, 1, 1}, 254}, {{13, 3, 2, 1, 1, 1, 1}, 255},           {{13, 3, 3, 1, 1, 1, 1}, 256}, {{13, 4, 1, 1, 1, 1, 1}, 257},           {{13, 4, 2, 1, 1, 1, 1}, 258}, {{13, 5, 1, 1, 1, 1, 1}, 259},           {{13, 6, 1, 1, 1, 1, 1}, 260}, {{14, 1, 1, 1, 1, 1, 1}, 261},           {{14, 2, 1, 1, 1, 1, 1}, 262}, {{14, 2, 2, 1, 1, 1, 1}, 263},           {{14, 2, 2, 2, 1, 1, 1}, 264}, {{14, 3, 1, 1, 1, 1, 1}, 265},           {{14, 3, 2, 1, 1, 1, 1}, 266}, {{14, 4, 1, 1, 1, 1, 1}, 267},           {{14, 5, 1, 1, 1, 1, 1}, 268}, {{15, 1, 1, 1, 1, 1, 1}, 269},           {{15, 2, 1, 1, 1, 1, 1}, 270}, {{15, 2, 2, 1, 1, 1, 1}, 271},           {{15, 3, 1, 1, 1, 1, 1}, 272}, {{15, 3, 2, 1, 1, 1, 1}, 273},           {{15, 4, 1, 1, 1, 1, 1}, 274}, {{16, 1, 1, 1, 1, 1, 1}, 275},           {{16, 2, 1, 1, 1, 1, 1}, 276}, {{16, 2, 2, 1, 1, 1, 1}, 277},           {{16, 3, 1, 1, 1, 1, 1}, 278}, {{16, 4, 1, 1, 1, 1, 1}, 279},           {{17, 1, 1, 1, 1, 1, 1}, 280}, {{17, 2, 1, 1, 1, 1, 1}, 281},           {{17, 2, 2, 1, 1, 1, 1}, 282}, {{17, 3, 1, 1, 1, 1, 1}, 283},           {{18, 1, 1, 1, 1, 1, 1}, 284}, {{18, 2, 1, 1, 1, 1, 1}, 285},           {{19, 1, 1, 1, 1, 1, 1}, 286}, {{19, 2, 1, 1, 1, 1, 1}, 287},           {{20, 1, 1, 1, 1, 1, 1}, 288}};       vector<string> DIST{            0 ,            10 ,            210 ,            3210 ,            43210 ,            543210 ,            6543210 ,            76543210 ,            211234560 ,            3211234510 ,            43211234210 ,            543211233210 ,            6543211243210 ,            76543211543210 ,            432223452112340 ,            5432223432112310 ,            65432223432112210 ,            765432225432113210 ,            8765432265432143210 ,            65433334432223211230 ,            765433335432223211210 ,            8765433365432243211210 ,            98765433765432543213210 ,            876544446543334322221120 ,            9876544476543354322321110 ,            21012345112345234564567670 ,            321012342112342234534565610 ,            4321012332112322234334545210 ,            54321012432112322233334443210 ,            654321015432114322233334443210 ,            7654321065432154322433344543210 ,            43211234210123112342345452112340 ,            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