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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;
import java.io.*;

class Main {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        long N = sc.nextLong();
        long tmp = (long)N+1;
        // double ans = 0;
        long ans2 = 0;
        boolean flag = false;

        /*for(int i = 1; i < Math.sqrt(N); i++){
            if(N % i == 0){
                ans = N / i;
                ans2 = (int)ans;
                tmp = Math.min(tmp,ans2+i);
            }
        }*/

        for(long i = 1; i < (N/2); i++){
            if(N % i == 0){
                ans2 = N / i;
                //ans2 = (int)ans;
                tmp = Math.min(tmp,ans2+i);
            }
        }

        System.out.println(tmp - 2);
    }
}