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>
namespace IO {
char ch = '\n';
template <class T>
inline T ReadInt() {
  T x(0);
  bool f(1);
  while (ch < '0' || '9' < ch) {
    if (ch == '-') {
      f = 0;
    }
    ch = getchar();
  }
  while ('0' <= ch && ch <= '9') {
    x = (x << 1) + (x << 3) + (ch ^ 48);
    ch = getchar();
  }
  return f ? x : -x;
}
template <class T>
inline T ReadUInt() {
  T x(0);
  while (ch < '0' || '9' < ch) {
    ch = getchar();
  }
  while ('0' <= ch && ch <= '9') {
    x = (x << 1) + (x << 3) + (ch ^ 48);
    ch = getchar();
  }
  return x;
}
inline double ReadDouble() {
  long long int_num = ReadInt<long long>();
  if (ch == '.') {
    double pow10 = 1, result = int_num;
    ch = getchar();
    while ('0' <= ch && ch <= '9') {
      pow10 /= 10.0;
      result += pow10 * (ch ^ 48);
      ch = getchar();
    }
    return result;
  } else {
    return (double)int_num;
  }
}
inline void ReadT(int &x) { x = ReadInt<int>(); }
inline void ReadT(long long &x) { x = ReadInt<long long>(); }
inline void ReadT(bool &x) { x = ReadUInt<bool>(); }
inline void ReadT(unsigned int &x) { x = ReadUInt<unsigned int>(); }
inline void ReadT(unsigned long long &x) { x = ReadUInt<unsigned long long>(); }
inline void ReadT(double &x) { x = ReadDouble(); }
inline void ReadT(char &s) {
  for (; isspace(ch) && (~ch); ch = getchar())
    ;
  s = ch;
  ch = '\n';
}
inline void ReadT(char *s) {
  int len(0);
  for (; isspace(ch) && (~ch); ch = getchar())
    ;
  for (; !isspace(ch) && (~ch); ch = getchar()) {
    s[len++] = ch;
  }
  s[len] = '\0';
  ch = '\n';
}
template <typename T>
inline void Read(T &t) {
  ReadT(t);
}
template <typename T, typename... Args>
void Read(T &t, Args &...args) {
  ReadT(t);
  Read(args...);
}
template <typename T>
void WriteInt(T x) {
  if (x < 0) {
    printf("-");
    x = -x;
  }
  if (9 < x) {
    WriteInt(x / 10);
  }
  putchar(x % 10 + '0');
}
template <typename T>
void WriteUInt(T x) {
  if (9 < x) {
    WriteInt(x / 10);
  }
  putchar(x % 10 + '0');
}
void WriteDouble(long double x, int len) {
  WriteInt((long long)x);
  if (len) {
    x -= (int)x;
    putchar('.');
    if (!x) {
      while (len--) {
        putchar(48);
      }
      return;
    }
    while (len--) {
      x *= 10;
    }
    WriteInt((long long)round(x));
  }
}
template <typename T>
inline void WriteT(T x);
template <>
inline void WriteT<int>(int x) {
  WriteInt<int>(x);
}
template <>
inline void WriteT<long long>(long long x) {
  WriteInt<long long>(x);
}
template <>
inline void WriteT<bool>(bool x) {
  WriteUInt<bool>(x);
}
template <>
inline void WriteT<unsigned int>(unsigned int x) {
  WriteUInt<unsigned int>(x);
}
template <>
inline void WriteT<unsigned long long>(unsigned long long x) {
  WriteUInt<unsigned long long>(x);
}
template <>
inline void WriteT<double>(double x) {
  WriteDouble(x, 6);
}
template <>
inline void WriteT<char *>(char *s) {
  int len(strlen(s));
  while (len--) {
    putchar(*s++);
  }
}
template <>
inline void WriteT<const char *>(const char *s) {
  while (*s) {
    putchar(*s++);
  }
}
template <>
inline void WriteT<char>(char x) {
  putchar(x);
}
template <typename T>
inline void Write(T t) {
  WriteT(t);
}
template <typename T, typename... Args>
void Write(T t, Args... args) {
  WriteT(t);
  Write(args...);
}
template <typename T>
inline void Writeln(T t) {
  WriteT(t);
  puts("");
}
template <typename T, typename... Args>
inline void Writeln(T t, Args... args) {
  WriteT(t);
  Write(args...);
  puts("");
}
inline void Writeln() { puts(""); }
const char NUMBER[36] = {'0', '1', '2', '3', '4', '5', '6', '7', '8',
                         '9', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H',
                         'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q',
                         'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z'};
template <typename T>
void WriteK(T x, int p) {
  if (x < 0) {
    printf("-");
    x = -x;
  }
  if (p <= x) {
    WriteK(x / p, p);
  }
  putchar(NUMBER[x % p]);
}
}  // namespace IO
using namespace IO;
using namespace std;
const int MAX_NUM = 1e5 + 5;
const int MAXN = 1e5 + 5;
int a, b, c;
namespace Prime {
bool notprime[MAX_NUM];
int prime[MAX_NUM];
int sum[MAX_NUM];
int num[MAX_NUM];
int cnt = 0;
void Calc(int top) {
  sum[1] = 1;
  for (int i = 2; i <= top; ++i) {
    if (!notprime[i]) {
      sum[i] = 2;
      num[i] = 1;
      prime[++cnt] = i;
    }
    for (int j = 1; j <= cnt && i * prime[j] <= top; ++j) {
      notprime[i * prime[j]] = 1;
      if (i % prime[j] == 0) {
        sum[i * prime[j]] = sum[i] / (num[prime[j]] + 1) * (num[prime[j]] + 2);
        ++num[i * prime[j]];
        break;
      } else {
        sum[i * prime[j]] = sum[i] << 1;
        num[i * prime[j]] = 1;
      }
    }
  }
}
}  // namespace Prime
long long Gcd(long long a, long long b) {
  if (!b) {
    return a;
  }
  return Gcd(b, a % b);
}
void Work() {
  Read(a, b, c);
  long long da = Prime::sum[a], db = Prime::sum[b], dc = Prime::sum[c],
            dab = Prime::sum[Gcd(a, b)], dbc = Prime::sum[Gcd(b, c)],
            dac = Prime::sum[Gcd(a, c)], dg = Prime::sum[Gcd(a, Gcd(b, c))];
  Writeln(da * db * dc - dab * (dab - 1) / 2 * dc - dbc * (dbc - 1) / 2 * da -
          dac * (dac - 1) / 2 * db + 4 * dg * (dg - 1) * (dg - 2) / 6 +
          2 * dg * (dg - 1) / 2 +
          dg * (dg - 1) * (dab + dbc + dac - 3 * dg) / 2 -
          (dab - dg) * (dbc - dg) * (dac - dg));
}
int main() {
  Prime::Calc(100000);
  int t;
  Read(t);
  for (int i = 1; i <= t; ++i) {
    Work();
  }
  return 0;
}
