Problem:
Score : 700 points

Problem Statement

You are given an integer N.
Build an undirected graph with N vertices with indices 1 to N that satisfies the following two conditions:

The graph is simple and connected.

There exists an integer S such that, for every vertex, the sum of the indices of the vertices adjacent to that vertex is S.

It can be proved that at least one such graph exists under the constraints of this problem.

Constraints

All values in input are integers.

3 \leq N \leq 100

Input

Input is given from Standard Input in the following format:

N

Output

In the first line, print the number of edges, M, in the graph you made. In the i-th of the following M lines, print two integers a_i and b_i, representing the endpoints of the i-th edge.

The output will be judged correct if the graph satisfies the conditions.

Sample Input 1

3

Sample Output 1

2
1 3
2 3

For every vertex, the sum of the indices of the vertices adjacent to that vertex is 3.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.File;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Properties;
import java.util.Scanner;
import java.util.Set;
import java.util.Stack;

public class Main {
	static Scanner sc = new Scanner(System.in);
	static Properties pps = System.getProperties();
	static boolean dbg = true;

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		int a = ni();
	
		List<String> l=new ArrayList<String>();
		solve(a,l);
		System.out.println(l.size());
		for(String str:l)
			out(str);
		
	}



	private static void solve(int a,List<String> l) {
		// TODO Auto-generated method stub
		
		if(a%2==0) {
			for(int i=1;i<=a/2;i++) {
				for(int j=i+1;j<=a/2;j++) {
					l.add(i+" "+j);
					l.add(i+" "+(a+1-j));
					l.add((a+1-i)+" "+j);
					l.add((a+1-i)+" "+(a+1-j));
				}
			}
		}
		else {
			solve(a-1, l);
			for(int i=1;i<a;i++) {
				l.add(a+" "+i);
			}
		}
		
	}



	private static void out(List<Integer> l) {
		// TODO Auto-generated method stub
		for (int i : l)
			System.out.println(i);

	}

	private static void out(int[] b) {
		// TODO Auto-generated method stub
		for (int i : b)
			System.out.println(i);

	}

	public static void out(String str) {

		if (dbg)
			System.out.println(str);
	}

	public static void out(int str) {

		if (dbg)
			System.out.println(str);
	}

	public static int ni() {

		return sc.nextInt();

	}

	public static String ns() {

		return sc.nextLine();
	}

	public static int[] ni(int k) {
		int[] res = new int[k];
		for (int i = 0; i < k; i++)
			res[i] = sc.nextInt();
		sc.nextLine();
		return res;
	}

	public static String[] ns(int k) {
		String[] res = new String[k];
		for (int i = 0; i < k; i++)
			res[i] = sc.nextLine();
		return res;
	}

	public static int[][] ni(int a, int b) {
		int[][] res = new int[a][b];
		for (int i = 0; i < a; i++)
			for (int j = 0; j < b; j++)
				res[i][j] = sc.nextInt();
		sc.nextLine();
		return res;
	}
}