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.

Example

Input

3


Output

2
1 3
2 3
/**
 * Created at 21:53 on 2019/03/23
 */

import java.io.*;
import java.util.*;
import java.math.BigInteger;

public class Main {

  static FastScanner sc = new FastScanner();

  public static void main(String[] args) {

    int N = sc.nextInt();

    int sum;
    if (N % 2 == 0) {
      sum = N - 1;
    } else {
      sum = N - 2;
    }

    System.out.println(N * (N-1) / 2 - N / 2);
    for (int i=0; i<N; i++) {
      for (int j=i+1; j<N; j++) {
        if (i + j != sum) System.out.println((i+1) + " " + (j+1));
      }
    }

  }

  static class Debugger {

    static long startTime;
    static boolean on = true;

    //入力受け取り後に呼び出す(入力時間をカウントしないため)
    static void start() {
      startTime = System.currentTimeMillis();
    }

    static void printTime() {
      if (on) System.out.println("(" + (System.currentTimeMillis() - startTime) + "ms)");
    }

    static void toggle() {
      on = !on;
    }

  }

  static class BigInt extends BigInteger {

    BigInteger MOD = new BigInteger("1000000007");
    static BigInt ZERO = new BigInt(0);
    static BigInt ONE = new BigInt(1);
    static BigInt TEN = new BigInt(10);

    public BigInt(long l) {
      super(Long.toString(l));
    }

    public BigInt(BigInteger i) {
      super(i.toByteArray());
    }

    public BigInt pow(int i) {
      return new BigInt(super.pow(i));
    }

    public BigInt[] divideAndRemainder(long l) {
      return divideAndRemainder(new BigInt(l));
    }

    public BigInt[] divideAndRemainder(BigInt i) {
      BigInt[] ret = new BigInt[2];
      BigInteger[] dAndR = super.divideAndRemainder(i);
      ret[0] = new BigInt(dAndR[0]);
      ret[1] = new BigInt(dAndR[1]);
      return ret;
    }

    public BigInt mod(long l) {
      return mod(new BigInt(l));
    }

    public BigInt mod(BigInt i) {
      return new BigInt(super.mod(i));
    }

    public BigInt mod() {
      return new BigInt(super.mod(MOD));
    }

    public BigInt add(long l) {
      return add(new BigInt(l));
    }

    public BigInt add(BigInt i) {
      return new BigInt(super.add(i));
    }

    public BigInt subtract(long l) {
      return subtract(new BigInt(l));
    }

    public BigInt subtract(BigInt i) {
      return new BigInt(super.subtract(i));
    }

    public BigInt multiply(long l) {
      return multiply(new BigInt(l));
    }

    public BigInt multiply(BigInt i) {
      return new BigInt(super.multiply(i));
    }

    public BigInt divide(long l) {
      return divide(new BigInt(l));
    }

    public BigInt divide(BigInt i) {
      return new BigInt(super.divide(i));
    }

    public BigInt abs() {
      return new BigInt(super.abs());
    }

  }

  /*
    add()でインデックスを指定しない場合指定されたソート順に違わない位置に追加する
    (ただしソートされていることが前提となる)
    Comparatorが0を返したとき、それらの順序は保証しない
    (TreeSet, TreeMapと違い削除はしない)
   */
  static class TreeList<E> extends ArrayList<E> {

    Comparator<? super E> comparator;

    TreeList(Comparator<? super E> c) {
      super();
      comparator = c;
    }

    /*
      ソート済みのリストに要素を追加する
     */
    public boolean add(E e) {
      int lowIndex = 0;
      int highIndex = size() - 1;
      int index = 0;

      if (size() == 0) {
        super.add(e);
        return true;
      }

      if (comparator.compare(e, get(0)) < 0) {
        index = 0;
      } else if (comparator.compare(e, get(highIndex)) > 0) {
        index = highIndex + 1;
      } else {
        while (lowIndex <= highIndex) {

          if (highIndex == lowIndex + 1 || highIndex == lowIndex) {
            index = highIndex;
            break;
          }

          int midIndex = (lowIndex + highIndex) / 2;
          ;

          if (comparator.compare(e, get(midIndex)) > 0) {
            lowIndex = midIndex;
          } else {
            highIndex = midIndex;
          }

        }
      }

      super.add(index, e);
      return true;
    }

  }

  static class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    private boolean hasNextByte() {
      if (ptr < buflen) {
        return true;
      } else {
        ptr = 0;
        try {
          buflen = in.read(buffer);
        } catch (IOException e) {
          e.printStackTrace();
        }
        if (buflen <= 0) {
          return false;
        }
      }
      return true;
    }

    private int readByte() {
      if (hasNextByte()) return buffer[ptr++];
      else return -1;
    }

    private static boolean isPrintableChar(int c) {
      return 33 <= c && c <= 126;
    }

    private void skipUnprintable() {
      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
    }

    public boolean hasNext() {
      skipUnprintable();
      return hasNextByte();
    }

    public String next() {
      if (!hasNext()) throw new NoSuchElementException();
      StringBuilder sb = new StringBuilder();
      int b = readByte();
      while (isPrintableChar(b)) {
        sb.appendCodePoint(b);
        b = readByte();
      }
      return sb.toString();
    }

    public long nextLong() {
      if (!hasNext()) throw new NoSuchElementException();
      long n = 0;
      boolean minus = false;
      int b = readByte();
      if (b == '-') {
        minus = true;
        b = readByte();
      }
      if (b < '0' || '9' < b) {
        throw new NumberFormatException();
      }
      while (true) {
        if ('0' <= b && b <= '9') {
          n *= 10;
          n += b - '0';
        } else if (b == -1 || !isPrintableChar(b)) {
          return minus ? -n : n;
        } else {
          throw new NumberFormatException();
        }
        b = readByte();
      }
    }

    public int nextInt() {
      return (int) nextLong();
    }
  }

}
