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
'''
def isPrime(n):
    l = int(sqrt(n))
    for i in range(2,l+1):
        if n%i == 0:
            return False
    return True
'''

limit = 1000000
isPrime = [True for i in range(limit + 1)]
isPrime[1] = False

p = 2
while p*p <= limit:
    if isPrime[p]:
        for i in range(2*p,limit+1,p):
            isPrime[i] = False
    p += 1

def isTprime(n):
    x = int(sqrt(n))
    if x*x == n:
        return isPrime[x]
    else:
        return False

n = int(input())
a = list(map(int,input().split()))
for i in a:
    if isTprime(i):
        res = "YES"
    else:
        res = "NO"
    print(res)