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 get_primes(k):
    l = list(range(k + 1))
    primes = []
    for i in range(2, k + 1):
        if l[i] != -1:
            j = l[i]
            primes.append(l[i])
            while l[i] * j <= k:
                l[l[i] * j] = -1
                j += 1 + l[i] % 2
    return primes
my_primes = get_primes(1000000)
my_primes_dict = {i * i: '' for i in my_primes}
answer = []
n = int(input())
array = list(map(int, input().split()))
for number in array:
    if number in my_primes_dict:
        answer.append('YES')
        answer.append('\n')
    else:
        answer.append('NO')
        answer.append('\n')
answer.pop()
print(''.join(answer))