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 <fstream>
#include <vector>
#include <cstring>
#include <algorithm> // sort
#include <map>
#include <cmath>

#define REP(i, n) for (long long i = 0; i < (n); i++) 
typedef long long ll;
static const ll MOD = 1000000007;
static const ll INF = 1000000000000000000LL;
using namespace std;

//約数のリストを返す

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

    ll res = INF;

    for(int i = 1; i <= sqrt(N); ++i)
    {
      if(N % i != 0)continue;

      res = min(res, i + N / i - 2);
    }

    cout << res << endl;

    return 0;    
}