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
import math as mt
input=sys.stdin.buffer.readline
#t=int(input())
mod=998244353
# Python3 function to 
# calculate nCr % p 
def ncr(n, r, p): 
	# initialize numerator 
	# and denominator 
	num = den = 1
	for i in range(r): 
		num = (num * (n - i)) % p 
		den = (den * (i + 1)) % p 
	return (num * pow(den, 
			p - 2, p)) % p 
def isPrime(n): 
      
    # Corner case 
    if n <= 1 : 
        return False
  
    # check from 2 to n-1 
    for i in range(2, n): 
        if n % i == 0: 
            return False
  
    return True
  

def printPrime(n): 
    p=[]
    for i in range(2, n + 1): 
        if isPrime(i): 
            p.append(i)
    return p      
MAXN = 1000000
  
# stores smallest prime factor for 
# every number 

spf = [0 for i in range(MAXN)] 
  
# Calculating SPF (Smallest Prime Factor)  
# for every number till MAXN. 
# Time Complexity : O(nloglogn) 
def sieve(): 
    spf[1] = 1
    for i in range(2, MAXN): 
          
        # marking smallest prime factor  
        # for every number to be itself. 
        spf[i] = i 
  
    # separately marking spf for  
    # every even number as 2 
    for i in range(4, MAXN, 2): 
        spf[i] = 2
  
    for i in range(3, mt.ceil(mt.sqrt(MAXN))): 
          
        # checking if i is prime 
        if (spf[i] == i): 
              
            # marking SPF for all numbers 
            # divisible by i 
            for j in range(i * i, MAXN, i):  
                  
                # marking spf[j] if it is  
                # not previously marked 
                if (spf[j] == j): 
                    spf[j] = i     
t=1
sieve()
for _ in range(t):
    n=int(input())
    #n,k=map(int,input().split())
    l=list(map(int,input().split()))
    for i in range(n):
        x=int(mt.sqrt(l[i]))
        if x*x==l[i] and x!=10**6:
            if spf[x]==x and x!=1:
                print("YES")
            else:
                print("NO")
        else:
            print("NO")