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 prime_check(num):
    limit = int(math.sqrt(num))+1

    counter = 0
    for divisor in range(2, limit):
        if num%divisor == 0:
            counter += 1

    if not counter:
        return True

    return False

n_input = input()
numbers = input()

numbers = numbers.split(' ')

for i in range(0, len(numbers)):
    num = int(numbers[i])
    test = int(math.sqrt(num)*100000)

    if (test%100000 != 0) | (test == 100000):
        print('NO')
    else:
        test = int(test/100000)

        if (test%2 == 0) & (test == 2):
            print('YES')
        elif (test%2 == 0) & (test != 2):
            print('NO')
        else:
            if prime_check(test):
                print('YES')
            else:
                print('NO')