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:
from collections import *
from sys import stdin
from math import *


def count_prime(n):
    prim = defaultdict(lambda: 1)
    prim[0] = prim[1] = 0
    i = 2
    while (i * i <= n):
        if prim[i]:
            for j in range(i * 2, n + 1, i):
                prim[j] = 0
        i += 1

    return prim


def arr_inp(n):
    if n == 1:
        return [int(x) for x in stdin.readline().split()]
    elif n == 2:
        return [float(x) for x in stdin.readline().split()]
    else:
        return [str(x) for x in stdin.readline().split()]


def pow1(x, base):
    if base == 0:
        return 1
    sq = pow1(x, base // 2)
    sq = (sq * sq)  # % num

    if base % 2:
        sq *= x
    return sq


primes = count_prime(1000000)

n, a = int(input()), arr_inp(2)

for i in a:
    s = int(sqrt(i))
    if i > 1 and s * s == i:
        if primes[s]:
            print('YES')
        else:
            print('NO')
    else:
        print('NO')