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: Time Limit Exceeded)

<?php
fscanf(STDIN, "%d", $n);

$prev = $n - 1;
for ($i = 1; $i < $n; $i++) {
  if ($n % $i === 0) {
    $count = $i + $n / $i - 2;
    if ($count > $prev) {
      echo $prev;
      exit;
    }
    $prev = $count;
  }
  if ($i > 100000000) {
    echo $prev;
    exit;
  }
}
echo $count;