- Time limit: 1.00 s
- Memory limit: 128 MB
Uolevi proposed the following conjecture:
Every positive integer that can be written as a sum of three distinct positive integers can be written as a sum of three equal positive integers.
To prove Uolevi wrong, Maija asked you to write a program to produce counterexamples for the conjecture.
In particular, given integer n, your program has to output the smallest positive integer that is larger than n and can be written as a sum of three distinct positive integers but can't be written as a sum of three equal positive integers.
Input
The only input line contains a single integer n.
Output
Output the smallest counterexample larger than n.
Constraints
- 0 \le n \le 10^7
Example
Input:
8
Output:
10
Explanation: Number 10 can be written as 2+3+5=10, but there is no positive integer x such that x+x+x=10.