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 <iostream>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <algorithm>
#include <string>
#include <cmath>
#include <cstdio>
#include <iomanip>
#include <fstream>
#include <cassert>
#include <cstring>
#include <unordered_set>
#include <unordered_map>
#include <numeric>
#include <ctime>
#include <bitset>
#include <complex>
#include <chrono>
#include <random>
#include <functional>

using namespace std;

#define rep(i, n) for (int i = 0; i < (n); ++i)
#define sz(x) int(x.size())
typedef long long ll;

using ipair = pair<int, int>;

ll INF = 1e16+7;
ll mod = 1e9+7;

bool operator>(const ipair a,const ipair b){return a.first > b.first;}


const double PI=3.14159265358979323846;

int main(){
  ll N;
  cin >> N;

  ll div = (ll)(sqrt(N)+1);

  ll found = -1LL;

  while(1){
    if(div == 1){
      found = 1LL;
      break;
    }
    if(N%div==0){
      found = div;
      break;
    }

    div--;
  }

  ll compliment = N / found;

  cout << (found-1) + (compliment-1) << endl;
  return 0;
}