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 PYTHON):

Solution:
import sys 

n = input() 

x = [0 for i in range(n)] 
x = map(int, sys.stdin.readline().split()) 

k = max(x)

is_prime = [1 for i in range((int(k**0.5))+2)] 
is_prime[0] = is_prime[1] = 0 

##print is_prime
##factors = [[1] for i in range(n+1)] 

def seive():
    
     global is_prime
     
     touched = [0 for i in range(len(is_prime))]
     
     n = len(is_prime)-1 
     
     for i in range(2, int(n**0.5)+2): 
     
         if not touched[i]: 
     
             is_prime[i] = 1 
             touched[i] = 1 
         
             for j in range(2*i, n+1, i): 
             
                 if not touched[j]: 
                 
                     is_prime[j] = 0 
                     touched[j] = 1
                     
                     
seive() 

allnum = set() 

for i in range((int(k**0.5)+2)): 
    if is_prime[i]: 
        allnum.add(i**2) 
        
s = '' 
for i in x: 

    if i in allnum: 
        s += 'YES\n'
       
    else: 
        s += 'NO\n' 
        
print s