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")
#pragma GCC target( \
    "sse,sse2,sse3,ssse3,sse4,sse4.1,sse4.2,popcnt,abm,mmx,avx,tune=native")
using namespace std;
const int MOD = 1000000007;
const int UNDEF = -1;
const int INF = 1 << 29;
template <typename T>
inline bool chkmax(T &aa, T bb) {
  return aa < bb ? aa = bb, true : false;
}
template <typename T>
inline bool chkmin(T &aa, T bb) {
  return aa > bb ? aa = bb, true : false;
}
int rint();
char rch();
long long rlong();
const int MAXN = 1e6 + 4;
const int MAXP = MAXN;
bool sieve_array[MAXP + 1];
int ap[MAXP + 1];
vector<int> gpv;
void sieve() {
  for (int i = 0; i <= MAXP; i++) {
    sieve_array[i] = true;
    ap[i] = 1 << 30;
  }
  sieve_array[0] = false;
  sieve_array[1] = false;
  int lim = (int)(ceil(sqrt(MAXP))) + 2;
  for (int i = 2; i <= lim; i++) {
    if (sieve_array[i]) {
      for (int j = i * i; j <= MAXP; j += i) {
        sieve_array[j] = false;
        ap[j] = i;
      }
    }
  }
  for (int i = 2; i <= MAXP; i++) {
    if (sieve_array[i]) {
      gpv.push_back(i);
      ap[i] = i;
    }
  }
}
const int mn = 1000000;
const int mk = 10;
const int md = 5000 + 1, mp = 41;
vector<vector<int> > f[md][mp];
int tmp[mk];
int factorize_tmp[500];
pair<int, int> factorize(int ox) {
  int x = ox;
  int tsz = 0;
  while (x > 1) {
    int p = ap[x];
    x /= p;
    factorize_tmp[tsz++] = p;
  }
  if (x > 1) factorize_tmp[tsz++] = x;
  sort(factorize_tmp, factorize_tmp + tsz);
  memset(tmp, 0, sizeof tmp);
  int didx = 0;
  int cnt = 0;
  for (int t = 0; t < tsz; t++) {
    int p = factorize_tmp[t];
    if (t == 0 || p != factorize_tmp[t - 1]) {
      tmp[didx++] = cnt;
      cnt = 0;
    }
    cnt++;
  }
  if (cnt) tmp[didx++] = cnt;
  sort(tmp, tmp + mk);
  pair<int, int> ans = make_pair(0, 0);
  for (int i = 0; i < mk / 2; i++) {
    ans.first *= 20;
    ans.first += tmp[i];
  }
  for (int i = mk / 2; i < mk; i++) {
    ans.second *= 20;
    ans.second += tmp[i];
  }
  return ans;
}
vector<pair<int, int> > vs;
int bins(vector<pair<int, int> > &v, pair<int, int> key) {
  int imin = 0, imax = v.size();
  while (imin < imax) {
    int imid = (imin + imax) >> 1;
    if (v[imid] < key)
      imin = imid + 1;
    else
      imax = imid;
  }
  return imin;
}
int h[785 + 2][md];
pair<int, int> x2p[mn + 1];
void init() {
  sieve();
  set<pair<int, int> > s;
  for (int x = 1; x <= mn; x++) {
    pair<int, int> got = factorize(x);
    x2p[x] = got;
    s.insert(got);
  }
  for (auto &w : s) {
    vs.push_back(w);
  }
  for (int si = 0; si < vs.size(); si++) {
    auto w = vs[si];
    vector<int> v;
    while (w.first) {
      v.push_back(w.first % 20);
      w.first /= 20;
    }
    while (w.second) {
      v.push_back(w.second % 20);
      w.second /= 20;
    }
    sort(v.begin(), v.end(), greater<int>());
    for (int d = 1; d < md; d++) {
      int final = INF;
      for (int p = 0; p < mp; p++) {
        for (auto &a : f[d][p]) {
          int ans = 0;
          int sz = min(a.size(), v.size());
          for (int i = 0; i < sz; i++) {
            ans += abs(a[i] - v[i]);
          }
          for (int i = sz; i < a.size(); i++) ans += a[i];
          for (int i = sz; i < v.size(); i++) ans += v[i];
          chkmin(final, ans);
        }
      }
      h[si][d] = final;
    }
  }
}
void makechain() {
  vector<int> emp;
  f[1][0].push_back(emp);
  for (int d = 2; d < md; d++) {
    for (int p = 1; p < mp; p++) {
      if (d % (p + 1)) continue;
      int x = d / (p + 1);
      for (int q = 0; q <= p; q++) {
        for (auto v : f[x][q]) {
          v.insert(v.begin(), p);
          f[d][p].push_back(v);
        }
      }
    }
  }
}
void solve() {
  int x = bins(vs, x2p[rint()]);
  int y = bins(vs, x2p[rint()]);
  int final = INT_MAX;
  for (int d = 1; d < md; d++) {
    int ans = h[x][d] + h[y][d];
    chkmin(final, ans);
  }
  printf("%d\n", final);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  makechain();
  init();
  int T = rint();
  for (int i = 0; i < T; i++) solve();
}
static char stdinBuffer[1024];
static char *stdinDataEnd = stdinBuffer + sizeof(stdinBuffer);
static const char *stdinPos = stdinDataEnd;
void readAhead(size_t amount) {
  size_t remaining = stdinDataEnd - stdinPos;
  if (remaining < amount) {
    memmove(stdinBuffer, stdinPos, remaining);
    size_t sz = fread(stdinBuffer + remaining, 1,
                      sizeof(stdinBuffer) - remaining, stdin);
    stdinPos = stdinBuffer;
    stdinDataEnd = stdinBuffer + remaining + sz;
    if (stdinDataEnd != stdinBuffer + sizeof(stdinBuffer)) *stdinDataEnd = 0;
  }
}
int rint() {
  readAhead(16);
  int x = 0;
  bool neg = false;
  while (*stdinPos == ' ' || *stdinPos == '\n') ++stdinPos;
  if (*stdinPos == '-') {
    ++stdinPos;
    neg = true;
  }
  while (*stdinPos >= '0' && *stdinPos <= '9') {
    x *= 10;
    x += *stdinPos - '0';
    ++stdinPos;
  }
  return neg ? -x : x;
}
char rch() {
  readAhead(16);
  while (*stdinPos == ' ' || *stdinPos == '\n') ++stdinPos;
  char ans = *stdinPos;
  ++stdinPos;
  return ans;
}
long long rlong() {
  readAhead(32);
  long long x = 0;
  bool neg = false;
  while (*stdinPos == ' ' || *stdinPos == '\n') ++stdinPos;
  if (*stdinPos == '-') {
    ++stdinPos;
    neg = true;
  }
  while (*stdinPos >= '0' && *stdinPos <= '9') {
    x *= 10;
    x += *stdinPos - '0';
    ++stdinPos;
  }
  return neg ? -x : x;
}