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

size = int(input())
nums = list(map(int, input().split()))

lim = 10**6
ar = [1]*(lim+1)

### T-Primes set
r = {4}

### Crivo de aristotenes
for i in range(2, lim):
    if ar[i] == 1:
        r.add(i*i)
        for j in range(i*i, lim, i): ### Cancela todos os multiplos de i
            ar[j] = 0

### Works but TLE

# def isPrime(n):
#     if n == 0 or n == 1:
#         return False
#     elif n == 2 or n == 3:
#         return True
#     elif n%2 == 0:
#         return False
#     else:
#         for i in range(3, int(math.sqrt(n))+1, 2):
#             if n%i == 0:
#                 return False
#
#         return True
#

for num in nums:
    if num in r:
        print("YES")
    else:
        print("NO")