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 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#include <iostream>
#include <string>
#include <vector>
using namespace std;

int main(void){
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);

  long long N;
  cin >> N;

  long long ans = N;
  for(long long i = 2; i <= sqrt(N); ++i) {
    if(N % i == 0) {
      ans = min(ans, (i - 1) + ((N / i) - 1));
    }
  }

  cout << ans << endl;

  return 0;
}