Description

Select several distinct positive integers whose total sum does not exceed $S$, so that the sum of the proper divisors (excluding the number itself) of all selected numbers is maximized.

Input Format

Input a positive integer $S$.

Output Format

Output the maximum possible sum of proper divisors.

11

9

Hint

【Sample Explanation】

Choose the numbers $4$ and $6$ to obtain the maximum value $(1+2)+(1+2+3)=9$.

【Constraints】

For $100\%$ of the testdata, $1 \le S \le 1000$.

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