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() {
  int n;
  cin >> n;
  unsigned long long int a;
  unsigned long long int temp;
  unsigned long long int temp2;
  unsigned long long int count = 0;
  for (int i = 0; i < n; i++) {
    cin >> a;
    if (a == 1) {
      cout << "NO\n";
    } else {
      temp = (unsigned long long int)sqrt(a);
      if (a == (temp * temp)) {
        temp2 = (unsigned long long int)sqrt(temp);
        if ((temp % 2 == 0) && (temp2 >= 2)) {
          count++;
          cout << "NO\n";
        } else {
          for (unsigned long long int j = 3; j <= temp2; j = j + 2) {
            if (temp % j == 0) {
              count++;
              cout << "NO\n";
              break;
            }
          }
        }
        if (count == 0) {
          cout << "YES\n";
        }
        count = 0;
      } else
        cout << "NO\n";
    }
  }
  return 0;
}