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 target("sse4.2")
using namespace std;
bool home = 1;
signed realMain();
mt19937 rng_home(0);
mt19937 rng_oj((long long)(new char));
int rng() {
  if (home) {
    return rng_home();
  } else {
    return rng_oj();
  }
}
unsigned long long rng_ull() {
  return (unsigned long long)rng() * rng() ^
         ((unsigned long long)rng() * rng());
}
int rng_range(int l, int r) { return l + abs(rng()) % (r - l + 1); }
signed main() {
  home = 0;
  if (home) {
    freopen("tony_stark", "r", stdin);
  } else {
    ios::sync_with_stdio(0);
    cin.tie(0);
  }
  realMain();
}
class linearSieve {
 public:
  vector<int> primes;
  vector<int> lp;
  void put(int Limit) {
    primes.clear();
    lp.clear();
    lp.resize(Limit + 1, 0);
    for (int i = 2; i <= Limit; i++) {
      if (!lp[i]) {
        lp[i] = i;
        primes.push_back(i);
      }
      for (int j = 0; j < (int)primes.size() && primes[j] * i <= Limit &&
                      primes[j] <= lp[i];
           j++) {
        lp[primes[j] * i] = primes[j];
      }
    }
  }
} user;
bool is_prime(int n) {
  if (n <= 1) return 0;
  for (int i = 2; i * i <= n; i++) {
    if (n % i == 0) return 0;
  }
  return 1;
}
const int N = 10000;
const int C = 500;
int dp[C][N], y, mxp;
queue<int> q[C];
map<vector<int>, int> id;
vector<int> primes;
int cnt = 0;
vector<int> v;
void gen(int sum = 29, int limit = (int)1e9, long long cur = 1, int prod = 1) {
  if (prod >= C) return;
  cnt++;
  id[v] = ++y;
  q[prod].push(id[v]);
  dp[prod][id[v]] = 0;
  mxp = max(mxp, prod);
  for (int j = 1; j <= min(sum, limit) &&
                  (long long)cur * primes[(int)v.size()] <= (long long)1e18;
       j++) {
    cur *= primes[(int)v.size()];
    v.push_back(j);
    gen(sum - j, j, cur, prod * (j + 1));
    v.pop_back();
  }
}
vector<int> so(vector<int> v) {
  assert(!v.empty());
  sort(v.rbegin(), v.rend());
  if (v.back() == 0) v.pop_back();
  return v;
}
vector<vector<int>> states(vector<int> v) {
  vector<vector<int>> ret;
  v.push_back(1);
  if (id.count(v)) ret.push_back(v);
  v.pop_back();
  for (int i = 0; i < (int)v.size(); i++) {
    if (i == 0 || (i > 0 && v[i] != v[i - 1])) {
      vector<int> v2(v), v3;
      v2[i]++;
      v3 = so(v2);
      if (id.count(v3)) ret.push_back(v3);
      v2[i] -= 2;
      v3 = so(v2);
      if (id.count(v3)) ret.push_back(v3);
    }
  }
  return ret;
}
vector<int> fo(int x) {
  vector<int> ret;
  while (x > 1) {
    int p = user.lp[x], cnt = 0;
    while (x % p == 0) {
      x /= p;
      cnt++;
    }
    ret.push_back(cnt);
  }
  sort(ret.rbegin(), ret.rend());
  return ret;
}
void print(vector<int> a) {
  for (auto &it : a) cout << it << " ";
  cout << "\n";
}
vector<int> sts[N];
signed realMain() {
  for (int i = 0; i < C; i++)
    for (int j = 0; j < N; j++) dp[i][j] = (int)1e9;
  user.put((int)1e6 + 7);
  for (int i = 1; i <= 10000; i++)
    if (is_prime(i)) primes.push_back(i);
  gen();
  assert(y < N);
  for (auto &it : id) {
    auto kek = states(it.first);
    for (auto &v : kek) {
      sts[it.second].push_back(id[v]);
    }
  }
  for (int c = 1; c < C; c++) {
    while (!q[c].empty()) {
      auto it = q[c].front();
      q[c].pop();
      for (auto &vec : sts[it]) {
        int relax = dp[c][it] + 1;
        if (dp[c][vec] == (int)1e9) {
          dp[c][vec] = relax;
          q[c].push(vec);
        }
      }
    }
  }
  int tests;
  cin >> tests;
  for (int tc = 1; tc <= tests; tc++) {
    int a, b;
    cin >> a >> b;
    vector<int> x = fo(a), y = fo(b);
    assert(id.count(x));
    assert(id.count(y));
    a = id[x];
    b = id[y];
    int best = (int)1e9;
    for (int j = 0; j < C; j++) {
      best = min(best, dp[j][a] + dp[j][b]);
    }
    cout << best << "\n";
  }
  return 0;
}