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:
import sys
from math import sqrt
input = sys.stdin.readline

############ ---- Input Functions ---- ############
def inp():
    return(int(input()))
def inlt():
    return(list(map(int,input().split())))
def insr():
    s = input()
    return(list(s[:len(s) - 1]))
def invr():
    return(map(int,input().split()))

def SieveOfEratosthenes(n): 
      
    # Create a boolean array "prime[0..n]" and initialize 
    # all entries it as true. A value in prime[i] will 
    # finally be false if i is Not a prime, else true. 
    prime = [True for i in range(n + 1)] 
    p = 2
    while (p * p <= n): 
          
        # If prime[p] is not changed, then it is a prime 
        if (prime[p] == True): 
              
            # Update all multiples of p 
            for i in range(p * 2, n + 1, p): 
                prime[i] = False
        p += 1
    prime[0]= False
    prime[1]= False
    # Print all prime numbers 
    for p in range(n + 1): 
        if prime[p]: 
            print(p)

def myVersionOfSieveOfEratosthenes(n):
    prime = [True for i in range(n + 1)] 
    prime[0] = prime[1] = False
    p = 2
    while (p * p <= n): 
        if (prime[p] == True): 
            for i in range(p * 2, n + 1, p): 
                prime[i] = False
        p += 1
    return prime

def checkPerfectSquare(n):
    root = sqrt(n)
    if int(root+0.5)**2 == n:
        return True
    else: 
        return False

t = int(input())
nums = list(map(int,input().split()))
n = 10**12
primeCheck = myVersionOfSieveOfEratosthenes(int(sqrt(n)))
for num in nums:
    if checkPerfectSquare(num):
        root = int(sqrt(num))
        if primeCheck[root]==True:
            print('YES')
        else:
            print('NO')
    else:
        print('NO')