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:
input()
d = [int(x) for x in input().split()]
out = []

from math import sqrt as fsqrt

def sqrt(x):
    f = int(fsqrt(x))
    if f * f == x:
        return f
    if (f+1) * (f+1) == x:
        return f+1
    return -1

pt = [1337,0,1,1,0,1,0,1,0,0,0]

def prime(x):
    if x < 10:
        return pt[x]
    for d in range(2, int(fsqrt(x)) + 2):
        if x % d == 0:
            return 0
    return 1

y = 'YES'
n = 'NO'

for x in d:
    xx = sqrt(x)
    if xx == -1:
        out.append(n)
        continue
    out.append(y if prime(xx) else n)

print('\n'.join(out))