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() {
  bool prime_squares[1000000 + 5];
  memset(prime_squares, true, sizeof(prime_squares));
  for (int i = 2; i * i <= 1000000 + 5; i++) {
    if (prime_squares[i] == true) {
      for (int j = i * i; j <= 1000000 + 5; j = j + i) {
        prime_squares[j] = false;
      }
    }
  }
  int n;
  cin >> n;
  unsigned long long int arr[n];
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
    long long int r = (long long int)sqrt(arr[i]);
    if (arr[i] != 1 && r * r == arr[i] && prime_squares[r] == true) {
      printf("YES\n");
    } else {
      printf("NO\n");
    }
  }
}