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:
import math
с = int(input())
numbers = list(map(int, input().split()))
PRIME_COUNT = 10 ** 6
is_prime = [True] * PRIME_COUNT
is_prime[0] = False
is_prime[1] = False
primes = [] 
for i in range(2, 1000):
    if is_prime[i]:
        for j in range(i * i, PRIME_COUNT, i):
            is_prime[j] = False
for elem in numbers:
    q = math.sqrt(elem)
    if (not q.is_integer()) or q >= 1000000 or (not is_prime[int(q)]):
        print("NO")
    else:
        print("YES")