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:
import math

def sieve(num):
    primes = [True for i in range(num)]
    primes[0], primes[1] = False, False
    for i in range(2, num):
        if primes[i]:
            for j in range(i*2, num, i):
                primes[j] = False

    return primes


def tprime(num):
    root = math.sqrt(num)
    if root % 1 != 0.0: return "NO"
    
    if primes[int(root)]: return "YES"

    return "NO"


n = int(input())
nums = [int(x) for x in input().split()]
primes = sieve(1000010)

for num in nums:
    print(tprime(num))