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 int xxx = 1000001;
  bool prime[xxx];
  memset(prime, true, sizeof(prime));
  for (long long int p = 2; p * p <= xxx; p++) {
    if (prime[p] == true) {
      for (long long int i = p * p; i <= xxx; i += p) prime[i] = false;
    }
  }
  set<long long int> sk;
  for (long long int p = 2; p <= xxx; ++p)
    if (prime[p]) sk.insert(p * p);
  long long int n;
  cin >> n;
  while (n--) {
    long long int temp;
    cin >> temp;
    auto it = sk.find(temp);
    if (it == sk.end())
      cout << "NO\n";
    else
      cout << "YES\n";
  }
}