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>
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops")
#pragma GCC optimize("no-stack-protector,fast-math")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
using namespace std;
const long long N = 1e6 + 100, OO = 1e9 + 7, M = 1e9 + 7, P = 6151, T = 2e3,
                SQ = 280, lg = 30;
long long mfac[N], tt[N], t[N], lv[T], nfac[T], d[T][T], nbest[T], mbest[T];
map<long long, long long> s;
vector<vector<long long> > vv;
vector<long long> tfac;
long long v(long long x) {
  long long cx = x;
  tfac.clear();
  while (x > 1) {
    long long m = mfac[x];
    long long c = 0;
    while (x % m == 0) c++, x /= m;
    tfac.push_back(c);
  }
  sort(tfac.begin(), tfac.end());
  long long tot = 0;
  for (long long r : tfac) tot = 30 * tot + r;
  tt[cx] = tot;
  return tot;
}
vector<long long> decomp(long long x) {
  vector<long long> res;
  while (x) res.push_back(x % 30), x /= 30;
  return res;
}
long long gfac(long long x) {
  vector<long long> v = decomp(x);
  long long res = 1;
  for (long long cfac : v) res *= (cfac + 1);
  return res;
}
long long gfac(vector<long long> v) {
  long long res = 1;
  for (long long cfac : v) res *= (cfac + 1);
  return res;
}
long long cdist(vector<long long> &v1, vector<long long> &v2) {
  long long rr = 0;
  for (long long i = 0; i < max((long long)v1.size(), (long long)v2.size());
       i++) {
    long long l = 0;
    if (i < (long long)v1.size()) l = v1[i];
    long long r = 0;
    if (i < (long long)v2.size()) r = v2[i];
    rr += abs(l - r);
  }
  return rr;
}
long long cdist(long long x, long long y) {
  vector<long long> v1 = decomp(x), v2 = decomp(y);
  long long rr = 0;
  for (long long i = 0; i < max((long long)v1.size(), (long long)v2.size());
       i++) {
    long long l = 0;
    if (i < (long long)v1.size()) l = v1[i];
    long long r = 0;
    if (i < (long long)v2.size()) r = v2[i];
    rr += abs(l - r);
  }
  return rr;
}
void buildvv(vector<long long> vcur) {
  vv.push_back(vcur);
  long long hi = 1000;
  if (vcur.size()) hi = vcur.back();
  long long cprod = 1;
  for (long long vval : vcur) cprod *= (vval + 1);
  hi = min(hi, 1000 / cprod);
  while (hi) {
    vcur.push_back(hi);
    buildvv(vcur);
    vcur.pop_back();
    hi--;
  }
}
int32_t main() {
  ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  for (long long i = 1; i < N; i++) mfac[i] = 1;
  for (long long i = 2; i < N; i++) {
    if (mfac[i] == 1) {
      mfac[i] = i;
      for (long long j = 2 * i; j < N; j += i) mfac[j] = i;
    }
  }
  for (long long i = 1; i < N; i++) {
    long long r = v(i);
    s[r];
  }
  vector<long long> empty;
  buildvv(empty);
  long long ntype = 0;
  for (auto it = s.begin(); it != s.end(); it++) {
    it->second = ntype;
    lv[ntype] = it->first;
    ntype++;
  }
  for (long long i = 1; i < N; i++) t[i] = s[tt[i]];
  long long fmax = 0;
  for (long long i = 0; i < ntype; i++) {
    for (long long j = 0; j < T; j++) d[i][j] = 1e9;
    vector<long long> itype = decomp(lv[i]);
    for (vector<long long> p : vv) {
      long long g = gfac(p);
      d[i][g] = min(d[i][g], cdist(itype, p));
    }
    nfac[i] = gfac(lv[i]);
    fmax = max(fmax, nfac[i]);
  }
  long long TT;
  cin >> TT;
  for (long long tst = 0; tst < TT; tst++) {
    long long a, b;
    cin >> a >> b;
    long long c1 = t[a], c2 = t[b];
    long long res = 1e9;
    for (long long i = 0; i < T; i++) res = min(res, d[c1][i] + d[c2][i]);
    cout << res << endl;
  }
}