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:
# 999966000289
limit = 1000000
primes = []
def isprime_upto():
    isprime = [True] * limit
    isprime[0] = isprime[1] = False
    for i in range(2,limit):
        if isprime[i] == True:
            for j in range(i*i, limit, i):
                isprime[j] = False
    return isprime                    

def check(n):
    if n == 4:
        return 1
    if n == 1 or n%2==0:
        return 0
    sqrt_n = n**0.5
    if sqrt_n==int(sqrt_n):
        if primes[int(sqrt_n)] == True:
            return 1
    return 0

if __name__=='__main__':
    primes = list(isprime_upto())
    cas = int(input())
    ar = list(map(int,input().split()))
    for i in ar:
        x = check(i)
        if x==1:
            print("YES")
        else:
            print("NO")