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 Sieve(n):
    prime = [True]*(n+1)
    p=2
    while(p*p<=n):
        if(prime[p]==True):
            for i in range(p*2,n+1,p):
                prime[i] = False
        p+=1
    prime[0] = False
    prime[1] = False
    return(prime)

n = int(input())
arr = list(map(int,input().split()))
x = []
val = Sieve(10**6)
#print(val)
for i in range(len(arr)):
    if(arr[i]**0.5==int(arr[i]**0.5)):
        #print("Hi")
        if(val[int(arr[i]**0.5)]):
            #print(arr[i]**0.5)
            x.append("YES")
        else:
            x.append("NO")
    else:
        x.append("NO")
for i in range(len(x)):
    print(x[i])