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: Accepted)

import java.util.*;

public class Main {
    final static int MOD = 1000000007;
    
    public static void main(String[] args) {
        MyScanner in = new MyScanner();
        long n = in.nextLong();
        long a = Long.MAX_VALUE;
        
        
        for (long i = 1; i * i <= n ; i++) {
            if (n % i == 0) {
                a = Math.min(a, (i + (n / i)));
            }
        }
    
        System.out.println(a-2);
        
    }
    
    static class MyScanner {
        static Scanner sc = new Scanner(System.in);
        
        String next() {
            return sc.next();
        }
        
        String nextLine() {
            return sc.nextLine();
        }
        
        int nextInt() {
            return Integer.parseInt(sc.next());
        }
        
        double nextDouble() {
            return Double.parseDouble(next());
        }
        
        long nextLong() {
            return Long.parseLong(next());
        }
        
        int[] nextIntArray(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; i++) {
                array[i] = nextInt();
            }
            return array;
        }
        
        double[] nextDoubleArray(int n) {
            double[] array = new double[n];
            for (int i = 0; i < n; i++) {
                array[i] = nextDouble();
            }
            return array;
        }
        
        long[] nextLongArray(int n) {
            long[] array = new long[n];
            for (int i = 0; i < n; i++) {
                array[i] = nextLong();
            }
            return array;
        }
        
        String[] nextLineArray(int n) {
            String[] array = new String[n];
            for (int i = 0; i < n; i++) {
                array[i] = nextLine();
            }
            return array;
        }
        
        int[][] nextIntMatrix(int n, int m) {
            int[][] matrix = new int[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    matrix[i][j] = nextInt();
                }
            }
            return matrix;
        }
        
        double[][] nextDoubleMatrix(int n, int m) {
            double[][] matrix = new double[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    matrix[i][j] = nextDouble();
                }
            }
            return matrix;
        }
        
        long[][] nextLongMatrix(int n, int m) {
            long[][] matrix = new long[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    matrix[i][j] = nextLong();
                }
            }
            return matrix;
        }
    }
}