Problem Description

Takahashi has $ n $ square tiles, each with a side length of $ 1 $ meter.

Takahashi wants to arrange some of these tiles without overlapping to form a large rectangle.

The resulting rectangle should be as close to a square as possible, but at the same time, he wants to minimize the number of leftover tiles.

What is the minimum sum of the absolute difference between the lengths of the sides of the rectangle and the number of leftover tiles?

Input Format

The input is given from the standard input in the following format:

$ n $

Output Format

Output the minimum value in one line.

Sample Input and Output

Sample Input #1

26

Sample Output #1

1

Sample Input #2

41

Sample Output #2

4

Sample Input #3

100000

Sample Output #3

37

Notes/Hints

Constraints

• $1 \leq n \leq 100,000$

Sample Explanation 1

Arranging the tiles to form a $5 \times 5$ square results in a difference of $ 0 $ between the lengths of the sides, and $ 1 $ leftover tile, making the sum $ 1 $. It is not possible to use all $ 26 $ tiles without leaving any leftover to form a square, so the answer is $ 1 $.

Sample Explanation 2

In this case, the optimal solution is to form a $5 \times 8$ rectangle with $ 1 $ leftover tile.

见题面 Input 部分

见题面 Output 部分