Identify Smith Numbers

A Smith number is a composite number, the sum of whose digits is the sum of the digits of its prime factors obtained as a result of prime factorization (excluding ). The first few such numbers are , , , , , , and .

Example:

So, its prime factors are , , , , and .
The sum of its digits is .
The sum of the digits of its factors is .

Similarly, is a Smith number.
, and the sum of its digits is the same as the sum of the digits of its prime factors: .

Task:
Write a program to check whether a given integer is a Smith number.

Input Format

There will be only one line of input: , the number which needs to be checked.

Constraints:
(max value of an integer of the size of bytes)

Output Format

if the number is a Smith number.
if the number is a not Smith number.

Sample Input

378

Sample Output

Explanation

Its prime factors are , , , , and .
The sum of its digits is .
The sum of the digits of its factors is .