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: Wrong Answer)

<?php

//文字列の入力
fscanf(STDIN,"%s",$n);

$lim = $n -1;

//2から始まる数字で$nを割り切れる数字がない場合、(1,n-1)となる
for ($i = 1; $i < $n; $i++){
    if ($n % $i == 0){
        $count = $i + $n/$i -2;
        if ($count > $lim){
            echo $lim;
            exit;
        }
        $lim = $count;
    }
    if ($i > 100000){
        echo $lim;
        exit;
    }
}

//2以降でnをあまり0で割り切れる数字がある場合
echo $count;