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 PYTHON):

Solution:
# -*- coding: utf-8 -*-
from math import sqrt

def sieve_prime(number):
    primes_sqrt = int(sqrt(number))
    primes = [True] * (number + 1)
    primes[0], primes[1] = False, False

    for i in xrange(2, primes_sqrt + 1):
        if primes[i]:
            for j in xrange(i * i, number + 1, i): primes[j] = False

    return primes

primes = sieve_prime(int(sqrt(10 ** 12)))
query = int(raw_input())
numbers = map(int, raw_input().split())

for number in numbers:
    square_root = sqrt(number)
    if square_root % int(square_root) != 0: print "NO"
    elif primes[int(square_root)]: print "YES"
    else: print "NO"