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

def prime(x):
    list = [1]*(x+1)
    list[0],list[1] = 0,0
    for i in range(2,int(math.sqrt(x))+1):
        if list[i] == 1:
            for j in range(i**2,x+1,i):
                list[j] = 0
    return list
#从0到x的质数表，list[i]==1时i为质数

a = int(input())
list = input().split()
primelist = prime(1000000)
for i in range(a):
    num = int(list[i])
    x = math.sqrt(num)
    print(['NO','YES'][x%1 == 0 and primelist[int(x)]])