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:
def change(a):
    b=a**0.5
    if b==1:
        return 0
    elif b%1==0:
        return int(b)
    else :
        return 0
plis=[1 for i in range (1000001)]
p=2
while p*p<=1000000:
    if plis[p]:
            for i in range(2*p,1000001,p):
                plis[i]=0
    p+=1

a=int(input())
lis1=list(map(int,input().split()))
lis2=list(map(change,lis1))
for i in lis2 :
    if i==0:
        print("NO")
    elif  plis[i]:
        print("YES")
    else :
        print("NO")