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:
#print(chr(9617))

import sys
from math import sqrt
input=sys.stdin.readline
print=sys.stdout.write

def prime():
    n = 10**6
    p = [True] * (n+1)
    p[1] = False
    i = 2
    while i*2 <= n:
        if p[i]:
            for k in range(i*2,n+1,i):
                p[k] = False
        i+=1

    return p

n = int(input())
a = list(map(int,input().split()))
def cal(num,p):
    yy = sqrt(num)
    if int(yy) == yy:
        if p[int(yy)]:
            return 0
        else:
            return 1
    else:
        return 1

p = prime()       
for i in range(n):
    print('YNEOS'[cal(a[i],p)::2]+'\n')