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:
from sys import stdin as inp
from sys import stdout as out
from math import sqrt
a=lambda:list(map(int,inp.readline().split()))
m=pow(10,6)
b=[True]*(m+1)
def check(x):
    l=1
    h=x
    ans=1
    while l<=h:
        m=(l+h)//2
        if m*m<=x:
            ans=m
            l=m+1
        else:
            h=m-1
    if ans*ans==x and b[ans]:
        return 'YES'
    return 'NO'
def seive():
    b[0]=False
    b[1]=False
    l=int(sqrt(m))+1
    for i in range(2,l):
        if b[i]:
            for j in range(i*i,m+1,i):
                b[j]=False
if __name__=='__main__':
    seive()
    n=a()[0]
    l=a()
    for i in l:
        out.write(check(i)+'\n')