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
list1 = []
n = 10**6 + 1
for a in range (2, n):
    list1.append(a)
p = 2
while p < math.sqrt(n) + 1:
    for a in range (pow(p, 2),n, p):
        list1[a - 2] = 0
    p += 1
    while list1[p-2]==0 and pow(p,2) < n:
        p += 1

a = int(input())
y = map(int,input().split())
list3 = []
for p in y:
    if p == 1:
        list3.append('NO')
    else:
        a = int(math.sqrt(p))
        if pow(a,2) == p:
            if list1[int(a-2)]:
                list3.append('YES')
            else:
                list3.append('NO')
        else:
            list3.append('NO')

for a in list3:
    print(a)