Problem: We know that prime numbers are positive integers that have exactly two distinct positive divisors. Similarly, we'll call a positive integer t Т-prime, if t has exactly three distinct positive divisors.

You are given an array of n positive integers. For each of them determine whether it is Т-prime or not.

Input

The first line contains a single positive integer, n (1 ≤ n ≤ 105), showing how many numbers are in the array. The next line contains n space-separated integers xi (1 ≤ xi ≤ 1012).

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is advised to use the cin, cout streams or the %I64d specifier.

Output

Print n lines: the i-th line should contain "YES" (without the quotes), if number xi is Т-prime, and "NO" (without the quotes), if it isn't.

Examples

Input

3
4 5 6


Output

YES
NO
NO

Note

The given test has three numbers. The first number 4 has exactly three divisors — 1, 2 and 4, thus the answer for this number is "YES". The second number 5 has two divisors (1 and 5), and the third number 6 has four divisors (1, 2, 3, 6), hence the answer for them is "NO".

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
int main() {
  int T;
  scanf("%d", &T);
  while (T--) {
    long long n;
    int m;
    scanf("%I64d", &n);
    m = sqrt(n);
    if ((long long)m * (long long)m != n || m == 1)
      puts("NO");
    else {
      int l = 0;
      for (int i = 2; i * i <= m; i++) {
        if (m % i == 0 && m != 2) {
          l = 1;
          break;
        }
      }
      if (l == 1)
        puts("NO");
      else
        puts("YES");
    }
  }
  return 0;
}