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
n=int(input())
arr=input().split()

sang=[]
Max=int(1e6)+1
for i in range(Max+1):
    sang.append(True)
sang[0]=sang[1]=False
j=2
while j*j<=Max:
    if sang[j]:
        k=j*j
        while k<=Max:
            sang[k]=False
            k+=j
    j+=1

for i in range(len(arr)):
    arr[i]=int(arr[i])
    temp= int(math.sqrt(arr[i]))
    if temp *temp ==arr[i] and arr[i]!=1 and sang[temp]:
        print("YES")
    else:
        print("NO")