We’re all familiar with harshad numbers. For this problem, you will ... what’s that? You aren’t familiar with harshad numbers? They’re also known as Niven numbers – does that ring a bell?? Anything???

Well, it’s a simple enough concept. A harshad number is a number which is evenly divisible by the sum of its digits. For example, $24$ is a harshad number: the sum of its digits is $2+4=6$ and $24$ is divisible by $6$. $156$ is also a harshad number, since $1+5+6=12$ and $156 = (12)(13$). $157$ is NOT a harshad number since it is not divisible by $1+5+7=13$.

OK, let’s start over.

We’re all familiar with harshad numbers. For this problem, you will be given a number $n$ and must find the smallest harshad number $\geq n$.

-----Input-----
Input consists of a single line containing a positive integer $n \leq 1000000000$.

-----Output-----
Display the smallest harshad number greater than or equal to $n$.

-----Examples-----
Sample Input 1:
24
Sample Output 1:
24

Sample Input 2:
25
Sample Output 2:
27

Source: kattis | Difficulty: EASY
Tags: Mathematics

Implementation


Solutions: