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:
# cook your dish here
import math 
n = int(input())
arr = [int(x) for x in input().split(" ")]
primes = []
limit =(10 **6)
is_primes =[True] * (limit+1)
is_primes[0]=False 
is_primes[1]= False
p = 2 
while p*p<= limit:
    if is_primes[p]:
        for i in range(p*2,limit+1,p):
            is_primes[i] = False 
    p+=1 


for val in arr:
    x = math.sqrt(val)
    if x==int(x) and is_primes[int(x)]:
        print ("YES")
    else:
        print("NO")
    
#print(is_primes[(10**6)])