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:
"""http://codeforces.com/problemset/problem/230/B"""

def sieve(n):
    s = [True] * (n + 1)
    for i in range(2, int(n ** 0.5) + 1):
        if s[i]:
            p = i * i
            while p <= n:
                s[p] = False
                p += i
    return set([4] + [x * x for x in range(3, n, 2) if s[x]])

def solve(arr):
    s = sieve(int(1e6))
    for i in arr:
        found = i in s
        print('YES' if found else 'NO')

def test_time():
    from random import randint
    from time import time
    start = time()
    solve((randint(1, 1e12) for _ in range(int(1e5))))
    print(time() - start)

if __name__ == '__main__':
    input(); solve(map(int, input().split()))