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 prime_check(long long x) {
  if (x == 1 || x == 0)
    return 0;
  else if (x == 2 || x == 3)
    return 1;
  else if (x % 2 == 0 || x % 3 == 0)
    return 0;
  else {
    for (int i = 5; i * i <= x; i += 6)
      if (x % i == 0 || x % (i + 2) == 0) return 0;
  }
  return 1;
}
int main() {
  int n;
  cin >> n;
  long long x, d;
  double d1;
  for (int i = 0; i < n; i++) {
    cin >> x;
    d1 = sqrt(x);
    d = d1;
    if (d == d1) {
      if (prime_check(d) == 1)
        cout << "YES\n";
      else
        cout << "NO\n";
    } else
      cout << "NO\n";
  }
  return 0;
}