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 ZDY {
#pragma GCC optimize(3)
template <class T>
__inline__ __attribute__((always_inline)) T ABS(T x) {
  return x > 0 ? x : -x;
}
template <class T>
__inline__ __attribute__((always_inline)) T MAX(T x, T y) {
  return x > y ? x : y;
}
template <class T>
__inline__ __attribute__((always_inline)) T MIN(T x, T y) {
  return x < y ? x : y;
}
template <class T>
__inline__ __attribute__((always_inline)) T GCD(T x, T y) {
  return y ? GCD(y, x % y) : x;
}
template <class T>
__inline__ __attribute__((always_inline)) void SWAP(T &x, T &y) {
  T t = x;
  x = y;
  y = t;
}
}  // namespace ZDY
using namespace ZDY;
using namespace std;
namespace IO {
const int str = 1 << 20;
static char in_buf[str], *in_s, *in_t;
bool __ = 0;
__inline__ __attribute__((always_inline)) char gc() {
  return (in_s == in_t) &&
             (in_t = (in_s = in_buf) + fread(in_buf, 1, str, stdin)),
         in_s == in_t ? EOF : *in_s++;
}
__inline__ __attribute__((always_inline)) void in(string &ch) {
  ch.clear();
  if (__) return;
  register char c;
  while ((c = gc()) != EOF && isspace(c))
    ;
  if (c == EOF) {
    __ = 1;
    return;
  }
  ch += c;
  while ((c = gc()) != EOF && !isspace(c)) ch += c;
  if (c == EOF) __ = 1;
}
__inline__ __attribute__((always_inline)) void in(char &ch) {
  if (__) return;
  register char c;
  while ((c = gc()) != EOF && isspace(c))
    ;
  if (c == EOF)
    __ = 1;
  else
    ch = c;
}
__inline__ __attribute__((always_inline)) void in(char *ch) {
  *ch = '\0';
  if (__) return;
  register char c;
  while ((c = gc()) != EOF && isspace(c))
    ;
  if (c == EOF) {
    __ = 1;
    return;
  }
  *ch = c;
  ch++;
  while ((c = gc()) != EOF && !isspace(c)) *ch = c, ch++;
  if (c == EOF) __ = 1;
  *ch = '\0';
}
template <typename T>
__inline__ __attribute__((always_inline)) void in(T &x) {
  if (__) return;
  register char c = gc();
  bool f = 0;
  while (c != EOF && (c < '0' || c > '9')) f ^= (c == '-'), c = gc();
  if (c == EOF) {
    __ = 1;
    return;
  }
  x = 0;
  while (c != EOF && '0' <= c && c <= '9') x = x * 10 + c - 48, c = gc();
  if (c == EOF) __ = 1;
  if (f) x = -x;
}
template <typename T, typename... arr>
__inline__ __attribute__((always_inline)) void in(T &x, arr &...y) {
  in(x), in(y...);
}
const char ln = '\n';
static char out_buf[str], *out_s = out_buf, *out_t = out_buf + str;
__inline__ __attribute__((always_inline)) void flush() {
  fwrite(out_buf, 1, out_s - out_buf, stdout);
  out_s = out_buf;
}
__inline__ __attribute__((always_inline)) void pt(char c) {
  (out_s == out_t) ? (fwrite(out_s = out_buf, 1, str, stdout), *out_s++ = c)
                   : (*out_s++ = c);
}
__inline__ __attribute__((always_inline)) void out(const char *s) {
  while (*s) pt(*s++);
}
__inline__ __attribute__((always_inline)) void out(char *s) {
  while (*s) pt(*s++);
}
__inline__ __attribute__((always_inline)) void out(char c) { pt(c); }
__inline__ __attribute__((always_inline)) void out(string s) {
  for (int i = 0; s[i]; i++) pt(s[i]);
}
template <typename T>
__inline__ __attribute__((always_inline)) void out(T x) {
  if (!x) {
    pt('0');
    return;
  }
  if (x < 0) pt('-'), x = -x;
  char a[50], t = 0;
  while (x) a[t++] = x % 10, x /= 10;
  while (t--) pt(a[t] + '0');
}
template <typename T, typename... arr>
__inline__ __attribute__((always_inline)) void out(T x, arr &...y) {
  out(x), out(y...);
}
}  // namespace IO
using namespace IO;
int n, d[100011], pri[100011], tot = 0, a[100011];
bool v[100011];
void sieve() {
  n = 100000;
  v[1] = 1;
  d[1] = 1;
  for (int i(2); i <= n; ++i) {
    if (!v[i]) pri[++tot] = i, a[i] = 1, d[i] = 2;
    for (int j = 1; j <= tot && i * pri[j] <= n; ++j) {
      v[i * pri[j]] = 1;
      if (i % pri[j])
        d[i * pri[j]] = d[i] * d[pri[j]], a[i * pri[j]] = 1;
      else {
        d[i * pri[j]] = d[i] / (a[i] + 1) * (a[i] + 2);
        a[i * pri[j]] = a[i] + 1;
        break;
      }
    }
  }
}
__inline__ __attribute__((always_inline)) long long Qjy(long long u) {
  return u * (u - 1);
}
int main() {
  sieve();
  int a, b, c;
  cin >> a >> b >> c;
  int ga = GCD(b, c), gb = GCD(a, c), gc = GCD(a, b), gg = GCD(ga, a);
  printf("%lld\n",
         d[a] * d[b] * d[c] -
             (d[a] * Qjy(d[ga]) + d[b] * Qjy(d[gb]) + d[c] * Qjy(d[gc]) >> 1) +
             (Qjy(d[gg]) * (d[gg] - 2) / 3 << 1) +
             (Qjy(d[gg]) * (d[ga] + d[gb] + d[gc] - 3 * d[gg] + 2) >> 1) -
             (d[ga] - d[gg]) * (d[gb] - d[gg]) * (d[gc] - d[gg]));
}
