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())
lst = list(map(int,input().split()))
maxnum = int(math.sqrt(max(lst)))
 
new = [1]*(maxnum+1)
new[0]=0
new[1]=0
for j in range(2,int(math.sqrt(maxnum))+1):
    if new[j]==1:
        for p in range(j*j,maxnum+1,j):
            new[p]=0
allprime=[]
for l in range(len(new)):
    if new[l]==1:
        allprime.append(l)
# print(allprime)
 
for i in lst:
#     print(new)
    A  = math.sqrt(i)
#     print(A)
#     print(new[int(A)])
    if A==int(A) and new[int(A)]==1:
        print('YES')
    else:
        print('NO')