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.*;
public class Main {
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    long a = sc.nextLong();

    long b = Long.MAX_VALUE /2;
    long c = Long.MAX_VALUE /2;
    List<Long> list = factorization(a);
    for (long i : list) {
        if((a/i + i) < (b + c) ){
          b = a/i;
          c = i;
        }
    }
    System.out.println(b + c -2);
  }

  static List<Long> factorization(long x) {
    List<Long> result = new ArrayList<>();

    while (x >= 4 && x % 2 == 0) {
        result.add((long)2);
        x /= 2;
    }
    long d = 3;
    long q = x / d;
    while (q >= d) {
        if (x % d == 0) {
            result.add(d);
            x = q;
        } else {
            d += 2;
        }
        q = x / d;
    }
    result.add(x);
    return result;
  }
}