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
from collections import Counter


def get(f):
    return map(f, input().split())


def divides(a, b):
    return a % b == 0


def sieve(upper):
    primes = []
    marked = [False for i in range(upper)]

    marked[0] = True
    marked[1] = True

    for i in range(2, upper):
        if not marked[i]:
            primes.append(i)

            for j in range(i, upper, i):
                marked[j] = True

    return primes


def main():
    n = int(input())
    nums = get(int)

    upper = int(1e6)
    primes = set(map(lambda x: x * x, sieve(upper)))

    for i in nums:
        if i in primes:
            print('YES')
        else:
            print('NO')


main()