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:
# Lang: pypy3.6-v7.1.0-win32\pypy3.exe
# Problem Name: T-primes
# Problem Serial No: 230
# Problem Type: B
# Problem Url: https://codeforces.com/problemset/problem/230/B 
# Solution Generated at: 2019-05-05 00:00:44.835358 UTC

def isPrime(n):
    if n<=1: return False
    elif n<=3: return True
    elif n%2==0 or n%3==0: return False
    i=5
    while i*i<=n:
        if n%i==0 or n%(i+2)==0: return False
        i+=6
    return True
if __name__ == '__main__':
    _=int(input())
    arr=list(map(int,input().split()))
    for k in arr:
        m = k ** 0.5
        if m==int(m):
            if isPrime(int(m)):
                print("YES")
            else:
                print("NO")
        else:
            print("NO")