You are given a rectangular parallelepiped with sides of positive integer lengths A, B and C. 

Find the number of different groups of three integers (a, b, c) such that 1≤ a≤ b≤ c and parallelepiped A× B× C can be paved with parallelepipeds a× b× c. Note, that all small parallelepipeds have to be rotated in the same direction.

For example, parallelepiped 1× 5× 6 can be divided into parallelepipeds 1× 3× 5, but can not be divided into parallelepipeds 1× 2× 3.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases.

Each of the next t lines contains three integers A, B and C (1 ≤ A, B, C ≤ 10^5) — the sizes of the parallelepiped.

Output

For each test case, print the number of different groups of three points that satisfy all given conditions.

Example

Input

4
1 1 1
1 6 1
2 2 2
100 100 100


Output

1
4
4
165

Note

In the first test case, rectangular parallelepiped (1, 1, 1) can be only divided into rectangular parallelepiped with sizes (1, 1, 1).

In the second test case, rectangular parallelepiped (1, 6, 1) can be divided into rectangular parallelepipeds with sizes (1, 1, 1), (1, 1, 2), (1, 1, 3) and (1, 1, 6).

In the third test case, rectangular parallelepiped (2, 2, 2) can be divided into rectangular parallelepipeds with sizes (1, 1, 1), (1, 1, 2), (1, 2, 2) and (2, 2, 2). 
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using Pii = pair<int, int>;
using Pll = pair<ll, ll>;
template <typename...>
static inline int getchar_unlocked(void) {
  return getchar();
}
template <typename...>
static inline void putchar_unlocked(int c) {
  putchar(c);
}
void reader(int& x) {
  int k, m = 0;
  x = 0;
  for (;;) {
    (k) = getchar_unlocked();
    if (k == '-') {
      m = 1;
      break;
    }
    if ('0' <= k && k <= '9') {
      x = k - '0';
      break;
    }
  }
  for (;;) {
    (k) = getchar_unlocked();
    if (k < '0' || k > '9') break;
    x = x * 10 + k - '0';
  }
  if (m) x = -x;
}
void reader(ll& x) {
  int k, m = 0;
  x = 0;
  for (;;) {
    (k) = getchar_unlocked();
    if (k == '-') {
      m = 1;
      break;
    }
    if ('0' <= k && k <= '9') {
      x = k - '0';
      break;
    }
  }
  for (;;) {
    (k) = getchar_unlocked();
    if (k < '0' || k > '9') break;
    x = x * 10 + k - '0';
  }
  if (m) x = -x;
}
int reader(char c[]) {
  int i, s = 0;
  for (;;) {
    (i) = getchar_unlocked();
    if (i != ' ' && i != '\n' && i != '\r' && i != '\t' && i != EOF) break;
  }
  c[s++] = i;
  for (;;) {
    (i) = getchar_unlocked();
    if (i == ' ' || i == '\n' || i == '\r' || i == '\t' || i == EOF) break;
    c[s++] = i;
  }
  c[s] = '\0';
  return s;
}
int reader(string& c) {
  int i;
  for (;;) {
    (i) = getchar_unlocked();
    if (i != ' ' && i != '\n' && i != '\r' && i != '\t' && i != EOF) break;
  }
  c.push_back(i);
  for (;;) {
    (i) = getchar_unlocked();
    if (i == ' ' || i == '\n' || i == '\r' || i == '\t' || i == EOF) break;
    c.push_back(i);
  };
  return ((int)c.size());
}
template <class T, class S>
void reader(T& x, S& y) {
  reader(x);
  reader(y);
}
template <class T, class S, class U>
void reader(T& x, S& y, U& z) {
  reader(x);
  reader(y);
  reader(z);
}
template <class T, class S, class U, class V>
void reader(T& x, S& y, U& z, V& w) {
  reader(x);
  reader(y);
  reader(z);
  reader(w);
}
void writer(int x, char c) {
  int s = 0, m = 0;
  char f[10];
  if (x < 0) m = 1, x = -x;
  while (x) f[s++] = x % 10, x /= 10;
  if (!s) f[s++] = 0;
  if (m) putchar_unlocked('-');
  while (s--) putchar_unlocked(f[s] + '0');
  putchar_unlocked(c);
}
void writer(ll x, char c) {
  int s = 0, m = 0;
  char f[20];
  if (x < 0) m = 1, x = -x;
  while (x) f[s++] = x % 10, x /= 10;
  if (!s) f[s++] = 0;
  if (m) putchar_unlocked('-');
  while (s--) putchar_unlocked(f[s] + '0');
  putchar_unlocked(c);
}
void writer(const char c[]) {
  int i;
  for (i = 0; c[i] != '\0'; i++) putchar_unlocked(c[i]);
}
void writer(const string& x, char c) {
  int i;
  for (i = 0; x[i] != '\0'; i++) putchar_unlocked(x[i]);
  putchar_unlocked(c);
}
void writer(const char x[], char c) {
  int i;
  for (i = 0; x[i] != '\0'; i++) putchar_unlocked(x[i]);
  putchar_unlocked(c);
}
template <class T>
void writerLn(T x) {
  writer(x, '\n');
}
template <class T, class S>
void writerLn(T x, S y) {
  writer(x, ' ');
  writer(y, '\n');
}
template <class T, class S, class U>
void writerLn(T x, S y, U z) {
  writer(x, ' ');
  writer(y, ' ');
  writer(z, '\n');
}
template <class T, class S, class U, class V>
void writerLn(T x, S y, U z, V v) {
  writer(x, ' ');
  writer(y, ' ');
  writer(z, ' ');
  writer(v, '\n');
}
template <class T>
void writerArr(T x[], int n) {
  if (!n) {
    putchar_unlocked('\n');
    return;
  }
  for (int i = 0; i < (n - 1); i++) writer(x[i], ' ');
  writer(x[n - 1], '\n');
}
template <class T>
void writerArr(vector<T>& x) {
  writerArr(x.data(), (int)x.size());
}
template <class T>
void chmin(T& a, const T& b) {
  if (a > b) a = b;
}
template <class T>
void chmax(T& a, const T& b) {
  if (a < b) a = b;
}
template <class T>
T gcd(T a, T b) {
  return b ? gcd(b, a % b) : a;
}
template <class T>
T lcm(T a, T b) {
  return a / gcd(a, b) * b;
}
ll mod_pow(ll a, ll n, ll mod) {
  ll ret = 1;
  ll p = a % mod;
  while (n) {
    if (n & 1) ret = ret * p % mod;
    p = p * p % mod;
    n >>= 1;
  }
  return ret;
}
template <class T>
T extgcd(T a, T b, T& x, T& y) {
  for (T u = y = 1, v = x = 0; a;) {
    T q = b / a;
    swap(x -= q * u, u);
    swap(y -= q * v, v);
    swap(b -= q * a, a);
  }
  return b;
}
ll mod_inv(ll a, ll m) {
  ll x, y;
  extgcd<ll>(a, m, x, y);
  return (m + x % m) % m;
}
int test(int a, int b, int c) {
  set<tuple<int, int, int>> st;
  for (int i = 0; i < (a + 1); i++)
    if (i != 0 && a % i == 0) {
      for (int j = 0; j < (b + 1); j++)
        if (j != 0 && b % j == 0) {
          for (int k = 0; k < (c + 1); k++)
            if (k != 0 && c % k == 0) {
              int cur[] = {i, j, k};
              sort(cur, cur + 3);
              st.emplace(cur[0], cur[1], cur[2]);
            }
        }
    }
  int x[] = {0, 0, 0, 0};
  for (auto abc : st) {
    int a, b, c;
    tie(a, b, c) = abc;
    if (a == b && b == c)
      x[0]++;
    else if (a == b && b < c)
      x[1]++;
    else if (a < b && b == c)
      x[2]++;
    else if (a < b && b < c)
      x[3]++;
    else {
      cout << "?";
    }
  }
  return ((int)st.size());
}
int cnt[((int)1e5) + 1];
void init() {
  for (int i = 1; i <= ((int)1e5); i++) {
    for (int j = i; j <= ((int)1e5); j += i) {
      cnt[j]++;
    }
  }
}
int solve(int x, int y, int z) {
  int g = cnt[gcd(gcd(x, y), z)];
  int d = cnt[gcd(x, y)] - g;
  int e = cnt[gcd(x, z)] - g;
  int f = cnt[gcd(y, z)] - g;
  int a = cnt[x] - d - e - g;
  int b = cnt[y] - d - f - g;
  int c = cnt[z] - f - e - g;
  int h[] = {a, b, c, d, e, f, g};
  int oks[3][7] = {
      {1, 0, 0, 1, 1, 0, 1},
      {0, 1, 0, 1, 0, 1, 1},
      {0, 0, 1, 0, 1, 1, 1},
  };
  bool used[7][7][7] = {};
  auto checkUsed = [&](int i, int j, int k) {
    if (i > k) swap(i, k);
    if (j > k) swap(j, k);
    if (i > j) swap(i, j);
    if (used[i][j][k]) return false;
    used[i][j][k] = true;
    return true;
  };
  int part[5] = {};
  int ans = 0;
  for (int i = 0; i < (7); i++)
    if (oks[0][i]) {
      for (int j = 0; j < (7); j++)
        if (oks[1][j]) {
          for (int k = 0; k < (7); k++)
            if (oks[2][k]) {
              if (!checkUsed(i, j, k)) {
                continue;
              }
              if (i != j && j != k && i != k) {
                int cur = h[i] * h[j] * h[k];
                ans += cur;
                part[0] += cur;
              } else if (i == j && j != k) {
                int cur = (h[i] - 1) * h[i] / 2 + h[i];
                cur *= h[k];
                ans += cur;
                part[1] += cur;
              } else if (i != j && j == k) {
                int cur = (h[j] - 1) * h[j] / 2 + h[j];
                cur *= h[i];
                ans += cur;
                part[2] += cur;
              } else if (i == k && j != k) {
                int cur = (h[k] - 1) * h[k] / 2 + h[k];
                cur *= h[j];
                ans += cur;
                part[3] += cur;
              } else {
                int aa = h[i];
                int bb = (h[i]) * (h[i] - 1) * (h[i] - 2);
                int cc = h[i] * h[i] * h[i] - aa - bb;
                int cur = aa + bb / 6 + cc / 3;
                ans += cur;
                part[4] += cur;
              }
            }
        }
    }
  return ans;
}
void test() {
  for (int i = 1; i <= 70; i++) {
    for (int j = 1; j <= 70; j++) {
      for (int k = 1; k <= 70; k++) {
        int a1 = test(i, j, k);
        int a2 = solve(i, j, k);
        if (a1 != a2) {
          cout << "?";
        }
      }
    }
  }
  cout << "ok" << endl;
}
int main() {
  init();
  int t;
  reader(t);
  while (t--) {
    int x, y, z;
    reader(x, y, z);
    int ans = solve(x, y, z);
    writerLn(ans);
  }
  return 0;
}
