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
n = int(input())
d = input().split(' ')
primes = [True]*1000005
primes[1] = False
primes[0] = False
for i in range(2,1000005,1):
    if primes[i] == True:
        for j in range(2*i,1000005,i):
            primes[j] = False
    if i*i >= 1000005:
        break

for i in range(0 , n  , 1):
    num = math.sqrt(int(d[i]))
    if math.ceil(num) != math.floor(num):
        print("NO")
    elif math.ceil(num) == math.floor(num) and int(num) == 1:
        print("NO")
    else:
        num = int(num)
        if primes[num] == True:
            print('YES')
        else:
            print('NO')