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
def sq(n):
    x=math.sqrt(n)
    if x-math.floor(x)==0:
        return int(x)
    else:
        return -1
def fun():
    prime=[True]*1000001
    prime[0]=False
    prime[1]=False
    for i in range(2,10001):
        if prime[i]==False:
            continue
        j=i
        while i*j<1000001: 
            prime[i*j]=False
            j+=1
    n=int(input())
    a=list(map(int,input().split()))
    for i in a:
        x=sq(i)
        if i==1:
            print("NO")
        else:
            if x!=-1:
                if prime[x]:
                    print("YES")
                else:
                    print("NO")
            else:
                print("NO")
fun()