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:
n = int(input())
nums = [int(i) for i in input().split()]


def prime_list(n):
    '''use sieve method to create a boolean list, so that order of growth is O(1)'''
    prime_bool = [True for i in range(n+1)]
    prime_bool[0], prime_bool[1] = False, False
    i = 2
    while i ** 2 <= n:
        if prime_bool[i]:
            for j in range(2*i, n, i):
                prime_bool[j] = False  # sieve!
        i += 1
    return prime_bool


prime_bool_list = prime_list(10**6+1)
for num in nums:
    if num ** 0.5 == int(num**0.5) and prime_bool_list[int(num**0.5)]:
        print('YES')
    else:
        print('NO')


# not useful
def all_primes(n): 
    '''create a list of all primes <= N'''
    is_existing = [True for i in range(n+1)]
    num, primes = 2, []
    while num ** 2 <= n:
        if is_existing[num]:
            primes.append(num)
            for i in range(num**2, n+1, num):
                is_existing[i] = False  # sieve!
        num += 1
    return primes


def is_prime(n):
    if n <= 1 or int(n) != n:
        return False
    else:
        i = 2
        while i ** 2 <= n:
            if n % i == 0:
                return False
            i += 1
        return True