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 prime(n):
    if (n <= 1) : 
        return 0
    if (n <= 3) : 
        return 1
    if (n % 2 == 0 or n % 3 == 0) : 
        return 0
    i = 5
    while(i * i <= n) : 
        if (n % i == 0 or n % (i + 2) == 0) : 
            return 0
        i = i + 6
    return 1
n=int(input())
a=[int(x) for x in input().split()]
for i in range(n):
    if(a[i]==4):
        print("YES")
    elif(a[i]%2==0):
        print("NO")
    else:
        res=int(a[i]**(0.5))
        #print(res)
        if(res*res==a[i]):
            if(prime(res)==1):
                print("YES")
            else:
                print("NO")
        else:
            print("NO")