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: Accepted)

#include <bits/stdc++.h>
using namespace std;
int main(){
  long n;
  cin >> n;
  int r;
  r = (int)sqrt(n) + 1;
  vector<vector<long>> v(1, vector<long>(3));
  v.at(0).at(0) = 1;
  v.at(0).at(1) = n;
  v.at(0).at(2) = 1 + n;
  for(int i = 1; i < r; i++){
    if(n % i == 0 && (i + n / i) < v.at(0).at(2) ){
      v.at(0).at(0) = i;
      v.at(0).at(1) = n / i;
      v.at(0).at(2) = i + n / i; 
    }
  }
  cout << v.at(0).at(2) - 2 << endl;
}