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:
# when the number can become T prime?
# if its square root is a prime

import math
from functools import lru_cache
from sys import stdin
input = stdin.readline

input(); l = [*map(int, input().split())]

@lru_cache(None)
def isPrime(n):
    for i in range(2, int(math.sqrt(n)) + 1):
        if n % i == 0:
            return False
    return True

for num in l:
    root = int(math.sqrt(num))
    if root ** 2 != num or num <= 2:
        print("NO")
        continue
    if isPrime(root):
        print("YES")
    else:
        print("NO")