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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

'use strict'

class Main {
  solve() {
    let n = input.nextIntArr()[0];
    const pairs = [];
    if (n % 2) pairs.push([n]);
    let m = n % 2 ? n - 1 : n;
    for (let i = 0; i < m/2; ++i) {
      pairs.push([i+1,m-i]);
    }
    let ret = [];
    for (let i = 0; i < pairs.length; ++i) {
      pairs[i].forEach((e1) => ret = ret.concat(pairs[(i+1)%pairs.length].map((e2) => [e1,e2])));
    }
    console.log(ret.length);
    console.log(ret.map((e)=>e.join(' ')).join('\n'));
  }
}

class Input {
  constructor() {
    this.cursor = 0;
    this.inputAll();
  }

  inputAll() {
    this.data = (require("fs").readFileSync("/dev/stdin", "utf8")).split('\n');
    return this.data;
  }

  /* 1行 or 複数行文字列 */
  nextLine(n) {
    if (n) {
      const ret = this.data.slice(this.cursor, this.cursor + n);
      this.cursor += n;
      return ret;
    }
    return this.data[this.cursor++];
  }
  /* 一行文字配列 */
  nextStrArr() { return this.nextLine().split(' '); } 
  /* 一行整数配列 */
  nextIntArr() { return this.nextStrArr().map((e) => parseInt(e)); }
  /* 一行浮動小数点配列 */
  nextFloatArr() { return this.nextStrArr().map((e) => parseFloat(e)); }
  /* 複数行整数配列 */
  nextIntLine(n) { return this.nextLine(n).map((e) => parseInt(e)) }
  /* 複数行浮動小数点配列 */
  nextFloatLine(n) { return this.nextLine(n).map((e) => parseFloat(e)) }
  /* 複数行文字列二次元配列 */
  nextStrRange(n) { return this.nextLine(n).map((line) => line.split(' ')); }
  /* 複数行整数二次元配列 */
  nextIntRange(n) {
    return this.nextLine(n).map((line) => line.split(' ').map((e) => parseInt(e)));
  }
  /* 複数行浮動小数点数二次元配列 */
  nextFloatRange(n) {
    return this.nextLine(n).map((line) => line.split(' ').map((e) => parseFloat(e)));
  }
} 
const input = new Input();
(new Main()).solve();