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:
input()
a = map(int, input().split())
N = 1000002
sieve = [0]+[1] * ((N // 2) + 1)
for j in range(1, ((N // 2) + 1)):
    if sieve[j]:
        p = 2*j+1
        for i in range(p*p, N, 2 * p):
            sieve[i//2] = 0

for v in a:
    r = round(v ** 0.5)
    if r * r == v:
        if sieve[r // 2] and (r % 2 or r == 2):
            print('YES')
            continue
    print('NO')