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:
from math import sqrt
import math
def Prime():
    primo = []
    for i in range(1000100):
        primo.append(True)
    primo[0] = False
    primo[1] = False

    for i in range(2,int(sqrt(1000100))+1):
        if(primo[i]):

            for j in range(i*i,1000100,i):
                primo[j] = False
    return primo

n = int(input())
l = list(map(int,input().split(None,n)[:n]))
primo = Prime()
for i in l:
    m = sqrt(i)
    k = math.fmod(m,int(m))
    if(k==0):
        if(primo[int(m)]):
            print('YES')
        else:
            print('NO')
    else:
        print("NO")

# 1534956480470