#include <bits/stdc++.h>
using namespace std;
const long long mod = 1e9 + 7;
int cnt, n, vis[305], a[305], C[305][305], sum[305];
map<int, int> m;
vector<int> v[305];
int num[305], top;
long long jie[305], ans, f[305][305];
void pre() {
  jie[0] = 1;
  for (int i = 1; i <= 300; i++) jie[i] = jie[i - 1] * i % mod;
  C[0][0] = 1;
  for (int i = 1; i <= 300; i++) {
    C[i][0] = C[i][i] = 1;
    for (int j = 1; j < i; j++) {
      C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % mod;
    }
  }
}
bool check(long long a) {
  long long temp = (long long)sqrt(a);
  return temp * temp == a;
}
void dfs(int a) {
  cnt++;
  vis[a] = 1;
  for (auto to : v[a]) {
    if (vis[to] == 0) dfs(to);
  }
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i];
  pre();
  for (int i = 1; i <= n; i++) {
    for (int j = i + 1; j <= n; j++) {
      if (check((long long)a[i] * a[j])) v[i].push_back(j);
    }
  }
  for (int i = 1; i <= n; i++) {
    cnt = 0;
    if (vis[i] == 0) {
      dfs(i);
      num[++top] = cnt;
    }
  }
  for (int i = 1; i <= top; i++) {
    sum[i] = sum[i - 1] + num[i];
  }
  f[0][0] = 1;
  for (int i = 1; i <= top; i++) {
    for (int j = 0; j <= 1 + sum[i - 1]; j++) {
      for (int k = 1; k <= num[i]; k++) {
        for (int p = 0; p <= min(k, j); p++) {
          f[i][j + num[i] - k - p] =
              (f[i][j + num[i] - k - p] +
               f[i - 1][j] * C[j][p] % mod * C[num[i] - 1][k - 1] % mod *
                   C[1 + sum[i - 1] - j][k - p] % mod) %
              mod;
        }
      }
    }
  }
  ans = f[top][0];
  for (int i = 1; i <= top; i++) {
    ans = ans * jie[num[i]] % mod;
  }
  cout << ans << endl;
  return 0;
}
