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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
  $n = trim(fgets(STDIN));
  $ans = 0;
  for ($i = 1; $i * $i <= $n; $i++) {
    $ama = $n % $i;
    if ($ama == 0) {
      $res = $n / $i;
      $tmp = ($res - 1) + ($i - 1);
      if ($ans == 0 || $tmp < $ans) {
        $ans = $tmp;
        continue;
      }
    }
  }
  echo $ans . PHP_EOL;