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 PYTHON):

Solution:
import sys
def nums():
    return map(int, raw_input().split())

def get_primes():
    N = 10**6 + 2
    isprime = [True] * N
    isprime[0] = isprime[1] = False
    i = 2
    while i*i < N:
        if isprime[i]:
            for j in xrange(i*i, N, i):
                isprime[j] = False
        i += 1
    ps = filter(lambda i:isprime[i], xrange(N))
    return ps, isprime

def test_t(x):
    q = x ** 0.5
    p = int(q)
    return bool(abs(q - p) < 1e-6 and isp[p])

ps, isp = get_primes()
minFac = {}

n = int(raw_input())
a = nums()
for x in a:
    print ('YES' if test_t(x) else 'NO')