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:
bs=['1']*(10**6+5)
from math import*
def seive (n):
    global bs
    bs[0]='0'
    bs[1]='0'
    for i in range (0,n):
        if (bs[i]=='1'):
            for j in range (i*i,n,i):
                bs[j]='0'


seive(1000000+2)

n = int(input())
l= list (map (int , input().split()))
for i in l:
    
    h = int (sqrt(i))   
    if (h*h==i and bs[h]=='1'):
        print("YES")
    else :
        print ("NO")