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 math import sqrt
prime=[*range(1000001)]
p=2
while p*p<1000001:
    if prime[p]!=-1:
        for i in range(p+p,1000001,p):
            prime[i]=-1
    p+=1
lol=[]
for i in range(2,1000001):
    if prime[i]!=-1:
        lol.append(i)
        
def search(n):
    low=1
    high=len(lol)
    f=0
    while low<=high and f==0:
        mid=(low+high)//2
        d=lol[mid-1]
        if d==n:
            f=1
            break
        elif d>n:
            high=mid-1
        else:
            low=mid+1
            
    return f        
x=int(input())
a=list(map(int,input().split()))
for i in range(x):
    q=sqrt(a[i])
    if q==int(q):
        q=int(q)
        k=search(q)
        if k==1:
            print("YES")
        else:
            print("NO")
    else:
        print("NO")