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: Runtime Error)

#include <bits/stdc++.h>
using namespace std;
  
int main(){
  int n,m;
  int i;
  int k,l;
  int a[13],b;
  
  cin >> n;
  a[0]=1;
  for(i=0;i<13;i++)
  {
    a[i+1]=10*a[i];
  }
  for(i=0;;i++)
  {
    
    if(n<=a[i]){
      b=i-1;
      break;
    }
    
  }
  
  for(i=a[b/2];i<=n;i++){
    
    if(i*i>=n){ 
      m=i;
      //cout<<j<<" "<<n<<" ";
      break;
    }
  }
  
  //cout<<m;
  
  for(i=m;;i--)
  {
    if(n%i==0){
      k=i;
      l=n/i;
      break;
    }    
  }

  cout<<k+l-2;

}