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
prime = [True for i in range(10**6 + 1)]
p = 2
while p*p <= 10**6:
    if prime[p]:
        for i in range(p*p, 10**6+1, p):
            prime[i] = False
    p += 1
n = int(input())
arr = [int(i) for i in input().split()]
for e in arr:
    if e > 1:
        r = e**0.5
        fr = math.floor(r)
        diff = r-fr
        if diff == 0 and prime[fr]:
            print("YES")
        else:
            print("NO")
    else:
        print("NO")