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 (7.4.4) (judge verdict: Accepted)

<?php
  list($n) = explode(" ", trim(fgets(STDIN)));

  $x = sqrt($n);
  $ans = -1;

  for($i=1; $i<=$x; $i++){
    if($n % $i == 0){
      $ans = $i;
    }
  }

  if($ans == -1){
    echo $n - 1;
    exit;
  }
  $p = $n / $ans ;
  echo $ans + $p - 2;