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:
def getInts():
    return [int(s) for s in input().split()]

def getInt():
    return int(input())

def getStrs():
    return [s for s in input().split()]

def getStr():
    return input()

def listStr():
    return list(input())

import math

n = 10**6
prime = [True for i in range(n + 1)] 
p = 2
while (p * p <= n): 
    if (prime[p] == True): 
        for i in range(p * 2, n + 1, p): 
            prime[i] = False
    p += 1
prime[0]= False
prime[1]= False
primes = dict()
for p in range(n,-1,-1): 
    if prime[p]: 
        primes[p]=p
    del prime[p]

def solve():
    N = getInt()
    A = getInts()
    for a in A:
        z = math.sqrt(a)
        if z == int(z) and z in primes:
            print("YES")
        else:
            print("NO")

solve()