#include <bits/stdc++.h>
using namespace std;
const int N = 305;
const int mod = 1e9 + 7;
int C[N][N];
int a[N];
int sz[N];
int F[N];
int dp[N][N];
int ptr = 0;
int n;
int solve(int idx, int badPairs, int total) {
  if (idx > ptr) return !badPairs;
  int &ret = dp[idx][badPairs];
  if (~ret) return ret;
  ret = 0;
  for (int i = 1; i <= min(total + 1, sz[idx]); i++) {
    for (int j = 0; j <= min(badPairs, i); j++) {
      int nxt = solve(idx + 1, badPairs + sz[idx] - i - j, total + sz[idx]);
      nxt = nxt * 1ll * F[sz[idx]] % mod;
      nxt = nxt * 1ll * C[sz[idx] - 1][i - 1] % mod;
      nxt = nxt * 1ll * C[badPairs][j] % mod;
      nxt = nxt * 1ll * C[total + 1 - badPairs][i - j] % mod;
      ret = (ret + nxt);
      if (ret >= mod) ret -= mod;
    }
  }
  return ret;
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 1; i <= n; i++)
    for (int j = 2; j * j <= a[i]; j++)
      while (a[i] % (j * j) == 0) a[i] /= (j * j);
  sort(a + 1, a + n + 1);
  for (int i = 1; i <= n; i++)
    if (a[i] != a[i - 1])
      sz[++ptr] = 1;
    else
      ++sz[ptr];
  for (int i = 0; i <= n; i++)
    for (int j = 0; j <= i; j++)
      C[i][j] = ((j == 0 || j == i) ? 1 : C[i - 1][j] + C[i - 1][j - 1]) % mod;
  F[0] = 1;
  for (int i = 1; i <= n; i++) F[i] = F[i - 1] * 1ll * i % mod;
  sort(sz + 1, sz + ptr + 1);
  memset(dp, -1, sizeof dp);
  cout << solve(2, sz[1] - 1, sz[1]) * 1ll * F[sz[1]] % mod << '\n';
  return 0;
}
