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
def inp(): return int(input())
def inps(): return map(int, input().split())
def is_sq(n): return pow(math.sqrt(n),2) == n
def sieve(n):
    np1 = n + 1
    s = list(range(np1)) 
    s[1] = 0
    sqrtn = int(round(n**0.5))
    for i in range(2, sqrtn + 1):
        if s[i]:
            s[i*i: np1: i] = [0] * len(range(i*i, np1, i))
    return set(filter(None, s))
    
n = inp()
primes = primes = sieve(1000006)
for i in inps() :
    if is_sq(i) :
        if math.sqrt(i) in primes :
            print("YES")
        else : print("NO")
    else: print("NO")