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;
bool visited[1000007] = {0};
vector<long long int> prime;
void process() {
  long long int i;
  for (i = 2; i < 1000007; i++) {
    if (visited[i] == 0) {
      visited[i] = 1;
      prime.push_back(i * i);
      for (auto j = i; j < 1000007; j += i) {
        visited[j] = 1;
      }
    }
  }
}
bool flag;
void binary(long long int a, long long int start, long long int end) {
  if (start > end) {
    return;
  }
  long long int mid = (start + end) / 2;
  if (prime[mid] == a) {
    flag = 1;
    return;
  } else {
    if (start == end) {
      return;
    } else {
      if (a < prime[mid]) {
        binary(a, start, mid);
      } else {
        binary(a, mid + 1, end);
      }
    }
  }
}
int main() {
  long long int n, m, temp, curr;
  cin >> n;
  process();
  long long int end = prime.size();
  for (auto i = 0; i < n; i++) {
    cin >> temp;
    flag = 0;
    binary(temp, 0, end);
    if (flag == 0) {
      cout << "NO" << endl;
    } else {
      cout << "YES" << endl;
    }
  }
  return 0;
}