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: Time Limit Exceeded)

#include <algorithm>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <vector>
using namespace std;
typedef long long ll;

#define rep(i, n) for(ll i = 0; i < n; i++)
#define REP(i, n) for(ll i = 1; i < n + 1; i++)
#define PI 3.14159265359
#define EPS 0.0000000001
#define MOD 1000000007
//cout << std::fixed << std::setprecision(15) << y << endl;


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

    ll a, b;
    a = 1;
    while(a * a <= N){
        a++;
    }
    a--;
    b = a;
    while(a * b != N){
        if(a * b > N){
            a--;
        }else{
            b++;
        }
    }

    cout << (a - 1) + (b - 1) << endl;

    return 0;
}