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: Wrong Answer)

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

  $fact = factorize($n);

  $h = 1;
  $w = 1;

  krsort($fact);

  foreach($fact as $f => $cnt){
    for($i=0; $i<$cnt; $i++){
      if($h > $w){
        $w *= $f;
      }else{
        $h *= $f;
      }
    }
  }
  echo $w-1+$h-1;

  function factorize($n){
    $res = [];
    for($i=2; $i*$i<=$n; $i++){
      if($n % $i != 0) continue;
      $res[$i]=0;
      while($n % $i == 0){      
        $res[$i]++;
        $n /= $i;
      }
    }
    if($n != 1){
      $res[$n]=1;
    }
    return $res;
  }