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:
n=int(input())
alnumber=list(map(int,input().split()))
mmax=max(alnumber)
halfmmax=int(mmax**(1/2))+1
alist=[True]*(halfmmax)
i=2
while i*2<halfmmax:
    if alist[i]:
        for p in range(2*i,halfmmax,i):
            
            alist[p]=False

    i+=1
for u in alnumber:
    halfnumber=u**(1/2)
    if halfnumber!=int(halfnumber) or u==1:
        print('NO')

    else:
        if alist[int(halfnumber)] :
            print('YES')
        else:
            print('NO')