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:
# https://codeforces.com/problemset/problem/230/B

"""
a t-prime is a number that has exactly three distinct positive divisors
Given an array of n positive integers, determine whether it is t-prime or not

Can only have three divisors if you were the square of a prime. As it would have factors
1, p, p**2

If we had more than one prime factor then we would have at least 4: 1, p, q, pq
"""

n = int(input())
X = list(map(int, input().split()))

# Only need to check up to sqrt of the max
limit = int(max(X) ** 0.5)
# Now find all primes up to this limit
prime = [True for i in range(limit + 1)]
p, prime[0], prime[1] = 2, False, False
while p * p <= limit:
    if prime[p]:
        for i in range(p * 2, limit + 1, p):
            prime[i] = False
    p += 1

for x in X:
    p = x ** 0.5
    if int(p) == p and prime[int(p)]:
        print('YES')
    else:
        print('NO')