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())
x=input()
y=x.split()
t=1000000
p=[True]*(t+1)
a=2
while (a*a<=t):
    if(p[a]==True):
        for i in range(a*2,t+1,a):
            p[i]=False
    a=a+1

for k in range(0,len(y)):
    u=int(y[k])
    v=u**.5
    if(u==1):
        print ('NO')
    elif(v%1==0):
        if(p[round(v)]==True):
            print ('YES')
        else:
            print ('NO')
    else:
        print ('NO')