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 PYTHON3):

Solution:
# URL: http://codeforces.com/problemset/problem/230/B

import math
from typing import List, Tuple, Set


def parse_input() -> Tuple[int, List[int]]:
    return int(input()), [int(x) for x in input().split()]


def find_primes(bound: int) -> Set[int]:
    sieve = [0, 0] + [1] * (bound - 2)
    bound_root = int(math.sqrt(bound)) + 1
    for i in range(2, bound_root):
        if sieve[i]:
            for j in range(i*i, bound, i):
                sieve[j] = 0
    return set([idx for idx, x in enumerate(sieve) if x])


def solve(xs: List[int]) -> List[str]:
    max_root = int(math.sqrt(max(xs))) + 1
    primes = find_primes(max_root)
    answer = []
    for x in xs:
        root = math.sqrt(x)
        if x % root == 0 and root in primes:
            answer.append("YES")
        else:
            answer.append("NO")
    return answer


if __name__ == '__main__':
    _, xs = parse_input()
    for elem in solve(xs):
        print(elem)