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:

def primeList():                                #check weather the sqrt is prime
    priList = [True] * 1000000
    priList[0] = priList[1] = False
    for i in range(2,1000000):
        if priList[i] == True:
            for j in range(i*i,1000000,i):
                priList[j] = False
    return priList


def isPrime(n):
    if n == 4:
        return True
    if n<4 or n%2 == 0:
        return False
    m = n**0.5
    if m==int(m):
        if pList[int(m)] == True:
            return True
    return False

pList = primeList()
s = int(input())
r = list(map(int,input().split()))
for i in r:
    if isPrime(i)== True:
        print('YES')
    else:
        print('NO')