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 PYTHON):

Solution:
primes=[]
def SieveOfEratosthenes(n): 
    prime=[True for i in xrange(n+1)] 
    p=2
    while (p*p<=n):           
        if (prime[p]==True): 
            for i in xrange(p*2,n+1,p): 
                prime[i]=False
        p+=1
    for p in xrange(2,n): 
        if prime[p]: 
            primes.append(p)
        else:
            primes.append("#")
n=(10**6)+1
SieveOfEratosthenes(n)
primes=["#","#"]+primes

import math
n=int(input())
l=list(map(int,raw_input().split()))
for i in xrange(len(l)):
    if l[i]==1:
        print"NO"
    else:
        x=(math.sqrt(l[i]))
        if int(x)==x:
            if primes[int(x)]!="#":
                print "YES"
            else:
                print"NO"
        else:
            print"NO"