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:
# MAGIC CODEFORCES PYTHON FAST IO
import atexit
import io
import sys

_INPUT_LINES = sys.stdin.read().splitlines()
input = iter(_INPUT_LINES).__next__
_OUTPUT_BUFFER = io.StringIO()
sys.stdout = _OUTPUT_BUFFER

@atexit.register
def write():
    sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())
# END OF MAGIC CODEFORCES PYTHON FAST IO

def tPrimos():
    TOPE_CRIBA = 1000000
    cribaArray = [True] * TOPE_CRIBA
    cribaArray[0] = cribaArray[1] = False
    for p in range(TOPE_CRIBA):
        if cribaArray[p]:
            for j in range(p*p, TOPE_CRIBA, p):
                cribaArray[j] = False
    return set(p*p for p in range(TOPE_CRIBA) if cribaArray[p])

def solve():
    yesSet = tPrimos()
    n = int(input())
    for number in map(int, input().split()):
        if number in yesSet:
            print("YES")
        else:
            print("NO")

solve()