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 collections import deque, Counter, OrderedDict
from heapq import nsmallest, nlargest
from math import ceil,floor,log,log2,sqrt,gcd,factorial
def binNumber(n,size=1):
    return bin(n)[2:].zfill(size)

def iar():
    return list(map(int,input().split()))

def ini():
    return int(input())

def isp():
    return map(int,input().split())

def sti():
    return str(input())

#  =========     /\       /|    |====/|
#      |        /  \       |    |   / |
#      |       /____\      |    |  /  |
#      |      /      \     |    | /   |
#  ========= /        \  =====  |/====|  
#  code

def checkprime(a):
    if a == 2 or a == 3:
        return True
    for i in range(2,int(ceil(sqrt(a)))+1):
        if a%i == 0:
            return False
    return True
if __name__ == "__main__":
    n = ini()
    a = iar()
    for i in a:
        if i == 1 or i == 2 or i == 3:
            print('NO')
            continue
        b = sqrt(i)
        c = int(b)
        if c == b:
            if checkprime(c):
                print('YES')
            else:
                print('NO')
        else:
            print('NO')