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:
#!python3

from collections import deque, Counter
from itertools import combinations, permutations
from math import sqrt
import unittest


def read_int():
    return int(input().strip())


def read_int_array():
    return [int(i) for i in input().strip().split(' ')]

######################################################

MAX = 10**6

def calc_primes(n):
    seive = [True] * n
    for i in range(3, int(n**0.5) + 1, 2):
        if seive[i]:
            seive[i*i::i*2]= [False] * ( (n - i*i - 1)//(i*2) + 1)
    return [2] + [i for i in range(3,n,2) if seive[i]]

primes = set(calc_primes(MAX))

n = read_int()
for m in read_int_array():
    is_tprime = m != 1 and m**0.5 % 1 == 0 and (m**0.5 in primes)
    print('YES' if is_tprime else 'NO')