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: Wrong Answer)

import java.util.*;
import java.lang.Math;

public class Main {
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        long n = s.nextLong();
        long l = 1;
        long i = (n / 2) - 1;
        //ここから下消すかも
        boolean sosuu = true;
        for (int a = 3; a < Math.sqrt(n); a += 2) {
            if (n % a == 0)
                sosuu=false;
        }
        if (!sosuu) {
            for (; i < (n + 1); i += 2) {
                if (n % i == 0) {
                    l = i;
                    break;
                }
            }
        }
        else if(sosuu){
            l=1;
        }
        System.out.println(l + (n / l) - 2);
    }
}