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 gcd(a):
		if (a <= 1):
			return -1; 
		for i in range(2,int(math.sqrt(a))+1):
			if (a % i == 0):
				return -1;
		return 0; 
n = int(input())
a = list(map(int, input().split(" ")))
for i in a:
    if (i==1):
        print ("NO")
        continue
    dou = math.sqrt(i)
    # print (dou)
    if (dou%1==0):
        dou = int(dou)
        d = gcd(dou)
        # print (d)
        if (dou==2):
            print ("YES")
        elif (d==0):
            print ("YES")
        else:
            print ("NO")
    else:
        print ("NO")