Problem: You are given two positive integers a and b. There are two possible operations: 

  1. multiply one of the numbers by some prime p; 
  2. divide one of the numbers on its prime factor p. 



What is the minimum number of operations required to obtain two integers having the same number of divisors? You are given several such pairs, you need to find the answer for each of them.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of pairs of integers for which you are to find the answer.

Each of the next t lines contain two integers a_i and b_i (1 ≤ a_i, b_i ≤ 10^6).

Output

Output t lines — the i-th of them should contain the answer for the pair a_i, b_i.

Example

Input

8
9 10
100 17
220 70
17 19
4 18
32 20
100 32
224 385


Output

1
3
1
0
1
0
1
1

Note

These are the numbers with equal number of divisors, which are optimal to obtain in the sample test case: 

  * (27, 10), 4 divisors 
  * (100, 1156), 9 divisors 
  * (220, 140), 12 divisors 
  * (17, 19), 2 divisors 
  * (12, 18), 6 divisors 
  * (50, 32), 6 divisors 
  * (224, 1925), 12 divisors 



Note that there can be several optimal pairs of numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1000100;
const int MAXT = 2000;
int mfac[MAXN];
long long tt[MAXN];
int t[MAXN];
long long lv[MAXT];
int nfac[MAXT];
int d[MAXT][MAXT];
map<long long, int> s;
vector<vector<int> > vv;
vector<int> tfac;
long long v(int x) {
  int cx = x;
  tfac.clear();
  while (x > 1) {
    int m = mfac[x];
    int c = 0;
    while (x % m == 0) {
      c++;
      x /= m;
    }
    tfac.push_back(c);
  }
  sort(tfac.begin(), tfac.end());
  long long tot = 0;
  for (int r : tfac) tot = 30 * tot + r;
  tt[cx] = tot;
  return tot;
}
vector<int> decomp(long long x) {
  vector<int> res;
  while (x) {
    res.push_back(x % 30);
    x /= 30;
  }
  return res;
}
int gfac(long long x) {
  vector<int> v = decomp(x);
  int res = 1;
  for (int cfac : v) res *= (cfac + 1);
  return res;
}
int gfac(vector<int> v) {
  int res = 1;
  for (int cfac : v) res *= (cfac + 1);
  return res;
}
int cdist(vector<int> &v1, vector<int> &v2) {
  int rr = 0;
  for (int i = 0; i < max(v1.size(), v2.size()); i++) {
    int l = 0;
    if (i < v1.size()) l = v1[i];
    int r = 0;
    if (i < v2.size()) r = v2[i];
    rr += abs(l - r);
  }
  return rr;
}
int cdist(long long x, long long y) {
  vector<int> v1 = decomp(x), v2 = decomp(y);
  int rr = 0;
  for (int i = 0; i < max(v1.size(), v2.size()); i++) {
    int l = 0;
    if (i < v1.size()) l = v1[i];
    int r = 0;
    if (i < v2.size()) r = v2[i];
    rr += abs(l - r);
  }
  return rr;
}
int nbest[MAXT], mbest[MAXT];
void buildvv(vector<int> vcur) {
  vv.push_back(vcur);
  int hi = 1000;
  if (vcur.size()) hi = vcur.back();
  int cprod = 1;
  for (int vval : vcur) cprod *= (vval + 1);
  hi = min(hi, 1000 / cprod);
  while (hi) {
    vcur.push_back(hi);
    buildvv(vcur);
    vcur.pop_back();
    hi--;
  }
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  for (int i = 1; i < MAXN; i++) mfac[i] = 1;
  for (int i = 2; i < MAXN; i++) {
    if (mfac[i] == 1) {
      mfac[i] = i;
      for (int j = 2 * i; j < MAXN; j += i) mfac[j] = i;
    }
  }
  for (int i = 1; i < MAXN; i++) {
    long long r = v(i);
    s[r];
  }
  vector<int> empty;
  buildvv(empty);
  int ntype = 0;
  for (auto it = s.begin(); it != s.end(); it++) {
    it->second = ntype;
    lv[ntype] = it->first;
    ntype++;
  }
  for (int i = 1; i < MAXN; i++) {
    t[i] = s[tt[i]];
  }
  int fmax = 0;
  for (int i = 0; i < ntype; i++) {
    for (int j = 0; j < MAXT; j++) d[i][j] = 1e9;
    vector<int> itype = decomp(lv[i]);
    for (vector<int> p : vv) {
      int g = gfac(p);
      d[i][g] = min(d[i][g], cdist(itype, p));
    }
    nfac[i] = gfac(lv[i]);
    fmax = max(fmax, nfac[i]);
  }
  int T;
  cin >> T;
  for (int test = 0; test < T; test++) {
    int a, b;
    cin >> a >> b;
    int c1 = t[a], c2 = t[b];
    int res = 1e9;
    for (int i = 0; i < MAXT; i++) {
      res = min(res, d[c1][i] + d[c2][i]);
    }
    cout << res << "\n";
  }
}