Problem:
Score : 300 points

Problem Statement

Takahashi is standing on a multiplication table with infinitely many rows and columns.

The square (i,j) contains the integer i \times j. Initially, Takahashi is standing at (1,1).

In one move, he can move from (i,j) to either (i+1,j) or (i,j+1).

Given an integer N, find the minimum number of moves needed to reach a square that contains N.

Constraints

2 \leq N \leq 10^{12}

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

Print the minimum number of moves needed to reach a square that contains the integer N.

Sample Input 1

10

Sample Output 1

5

(2,5) can be reached in five moves. We cannot reach a square that contains 10 in less than five moves.

Sample Input 2

50

Sample Output 2

13

(5, 10) can be reached in 13 moves.

Sample Input 3

10000000019

Sample Output 3

10000000018

Both input and output may be enormous.

Solution in PHP (5.6.30) (judge verdict: Accepted)

<?php
 // Your code here!
    # 整数の入力
    fscanf(STDIN, "%d", $i);
    $j = floor(sqrt($i));
    if ($i % $j == 0) {
        $k = $i / $j;
        echo ($k + $j - 2);
    } else {
        for ($j; $j--;) {
            if ($i % $j == 0) {
                $k = $i / $j;
                break;
            };
        };
        echo ($k + $j - 2);
    };
  ?>