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 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <stdio.h>

int kaijo(int x){
  int M=1, i;
  if(x==0){
    return 1;
  }else{
  	for(i=1;i<=M;i++){
    	M=M*i;
  	}
  return M;
  }
}
 
int main(void){
  int N, i, j, k, l, min, a[1000000000001], b[1000000000001];
  scanf("%d", &N);
  for(i=1;i<=N;i++){
    a[i] = N/(i);
  }
  for(j=1;j<=N;j++){
    b[j]=(kaijo(a[j]+j))/(kaijo(a[j])*kaijo(j));
  }
  min = b[1];
  for(k=1;k<=N;k++){
    for(l=k+1;l<=N;l++){
      if(b[l]<=b[k]){
        min = b[l];
      }
    }
  }
  printf("%d", min);
  
  return 0;
}