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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
  int main(void){
  int N;
  scanf("%d", &N);
  int i_past = 1;
  int j_past = N;
  //printf("%d\n",N + 1);
  int last;
  for(int i = 1; i <= N / 2 + 1; i++){
  	int k = N % i;//ここでiに対するjを取得する。余りが０ならｊが得られる。
  	//printf("i_past %d\n",i_past);
  	
  	if(k == 0){
          int j = N / i;//j取得
  		if(i + j <= i_past + j_past){
  			i_past = i;
  			j_past = j;
  			last = i_past + j_past - 2;//移動回数を求める
	  	}//i+jが以前のものより小さかった場合、i,jをi_past,j_pastとして保存する
  	// printf("i %d\n",i_now);
  	// last = i_past + j_past - 2;//移動回数を求める
      }
    
  	// printf("i_past %d\n",i_past);
  }
  printf("%d", last);
  //printf("i_past %d j_past %d",i_past, j_past);
  
  return 0;
}