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:
# so what have a positive divisors?
# a prime number have 2 divisors
# so how can we add one to that?
# the way i see it is if we squared any prime number, that will make it divisible by:
# 1- 1
# 2- the prime number
# 3- the prime number square
# example: 3 ==> 9 [1, 3, 9] 

# since i got timeout error when i tried to check if a number is prime [using a sqrt(n) loop]
# the only way left is to generate a stream of prime number [it will be somewhat fast since the limit is sqrt(10**12)]
# the algo used is the famous Sieve of Eratosthenes to return a list of True, False values
# of numbers from 0 to 10**6, so each index states if it's prime or not    

n = int(input())

def SOE(n):
    l = 2*[False] + (n-1)*[True]
    for i in range(2, int(n**0.5)+1):
        for j in range(i*i, n+1, i):
            l[j] = False
    
    return l

primes = SOE(10**6)

for i in map(int, input().split()):
    if int(i**0.5) == float(i**0.5):
        if primes[int(i**0.5)] == True:
            print ('YES')
        else:
            print ('NO')
    else:
        print ('NO')