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 math import sqrt

memo = dict()
memo[0], memo[1] = False, False
def isPrime(N):
    if N in memo:
        return memo[N]
    rt = int(sqrt(N))
    cnt = 0
    for i in range(1, rt + 1):
        if N % i == 0:
            cnt += 1
    memo[N] = True if cnt <= 1 else False
    return memo[N]

N = int(input())
# print(f'N: {N}')
nums = [int(x) for x in input().split()]
for n in nums:
    rt = sqrt(n)
    # print(f'rt: {int(rt)}')
    # print(f'rt.is_integer(): {rt.is_integer}')
    # print(f'isPrime(rt): {isPrime(int(rt))}')
    # print(f'rt * rt = {int(rt * rt)}')
    if rt.is_integer() and isPrime(int(rt)) and int(rt * rt) == n:
        print('YES')
    else:
        print('NO')