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 sys

input = sys.stdin.readline
dp = [False] * 1000001

def inp():
    return (int(input()))


def inlt():
    return (list(map(int, input().split())))


def build_sieve():
    dp[1] = True
    for i in range(2, 1000):
        if not dp[i]:
            j = 2
            while i * j <= 1000000:
                dp[i*j] = True
                j += 1


def solve(arr):
    for a in arr:
        if a in [1,2,3]:
            print("NO")
            continue
        if a == 4:
            print("YES")
            continue
        if a % 2 == 0:
            print("NO")
            continue
        sq = a ** 0.5
        if not sq.is_integer():
            print("NO")
            continue
        if dp[int(sq)]:
            print("NO")
            continue
        print("YES")


if __name__ == '__main__':
    n = inp()
    build_sieve()
    arr = inlt()
    solve(arr)