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

maxsize = 1000001

candidates = [True] * maxsize
sqrts = [0] * maxsize


for i in range(2, maxsize):
    if(candidates[i]):
        sqrts[i] = 1
        # sqrts.append(i**2)
        for j in range(i**2, maxsize, i):
            candidates[j] = False

# print(candidates)
# print(sqrts)

n = int(input())

xs = input().split(' ')


for i in xs:
    # print(xs)
    # print(sqrts)
    i = int(i)
    sqrt = math.sqrt(i)
    # if(i != 4 and i % 2 == 0):
    #     print("NO")
    # else:
    if(sqrt == int(sqrt) and sqrts[int(sqrt)] == 1):
        print("YES")
    else:
        print("NO")