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
import itertools

gh = lambda: map( int, input().split() )
N = 2 * 1e7 + 5
N = int(N)

def main():
    input()
    d = [0] * N
    d[1] = 1
    for i in range( 2, int( 1e4 ) ):
        if d[i] == 0:
            for j in range( i + i, int( 2e6 ), i ):
                d[j] = 1
    for x in gh():
        t = int( math.sqrt( x ) )
        bl = d[t]
        if t != math.sqrt(x): bl = 1
        if bl:
            print( "NO" )
        else: print( "YES" )

main()