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>
void PrintArr(int *arr, long long int size) {
  for (size_t i = 0; i < size; i++) {
    printf("%d:%d ", i, arr[i]);
  }
  printf("\n");
}
int main() {
  int test;
  scanf("%d", &test);
  long long int numbers[test];
  long long int max = 0;
  for (size_t i = 0; i < test; i++) {
    scanf("%I64d", &numbers[i]);
    if (numbers[i] > max) {
      max = numbers[i];
    }
  }
  max = pow(max, 0.5);
  int *primes = (int *)calloc(max + 1, sizeof(int));
  long long int index = 2;
  while (index <= max) {
    if (primes[index] == 0) {
      long long int tempindex = index * 2;
      while (tempindex <= max) {
        primes[tempindex] = 1;
        tempindex += index;
      }
    }
    index++;
  }
  long double x;
  long long int y;
  for (size_t i = 0; i < test; i++) {
    x = pow(numbers[i], 0.5);
    y = x;
    if (x != y || y == 1) {
      printf("NO\n");
      continue;
    }
    if (primes[y] == 0) {
      printf("YES\n");
    } else {
      printf("NO\n");
    }
  }
  return 0;
}