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>
using namespace std;
int main() {
  long long t, n, m, f, i;
  cin >> t;
  while (t--) {
    cin >> n;
    m = sqrt(n);
    if (m * m == n) {
      f = 0;
      if (m <= 1) {
        f = 1;
      } else if (m <= 3) {
        f = 0;
      } else if (m % 2 == 0 || m % 3 == 0) {
        f = 1;
      } else {
        for (int i = 5; i * i <= m; i = i + 6)
          if (m % i == 0 || m % (i + 2) == 0) f = 1;
      }
      if (f == 0) {
        cout << "YES" << endl;
      } else {
        cout << "NO" << endl;
      }
    } else {
      cout << "NO" << endl;
    }
  }
}