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>
int compare(const void *a, const void *b) {
  if (*(unsigned long long *)a > *(unsigned long long *)b) {
    return 1;
  } else if (*(unsigned long long *)a < *(unsigned long long *)b) {
    return -1;
  } else {
    return 0;
  }
}
int cnt;
unsigned long long *getList() {
  unsigned long long *list = 0;
  unsigned long long i = 0, j = 0;
  char isPrime[1000000 + 1] = {
      0,
  };
  memset(isPrime, 1, 1000000 + 1);
  isPrime[0] = isPrime[1] = 0;
  for (i = 2; i <= 1000000; i++) {
    if (isPrime[i]) {
      cnt++;
      for (j = i * 2; j <= 1000000; j += i) {
        isPrime[j] = 0;
      }
    }
  }
  list = (unsigned long long *)malloc(sizeof(unsigned long long) * cnt);
  int index = 0;
  for (i = 2; i <= 1000000; i++) {
    if (isPrime[i]) {
      list[index++] = i * i;
    }
  }
  return list;
}
int main(void) {
  unsigned long long *list = getList();
  int n = 0;
  unsigned long long num = 0;
  scanf("%d", &n);
  while (n--) {
    scanf("%llu", &num);
    if (bsearch(&num, list, cnt, sizeof(unsigned long long), compare)) {
      printf("YES\n");
    } else {
      printf("NO\n");
    }
  }
  free(list);
  return 0;
}