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
import java.io.*;
import java.util.*;

public class Main {
  private static List<String> solve4k1(int n) {
    List<String> list = new ArrayList<>();
    for (int i = 1; i <= n; i++) {
      for (int j = i+1; j <= n; j++) {
        if (i + j != n) {
          list.add(String.format("%d %d", i, j));
        }
      }
    }
    return list;
  }
  
  private static List<String> solve4k2(int n) {
    List<String> list = new ArrayList<>();
    for (int i = 1; i <= n; i++) {
      for (int j = i+1; j <= n; j++) {
        if (i + j != n + 1) {
          list.add(String.format("%d %d", i, j));
        }
      }
    }
    return list;
  }
  
  private static List<String> solve4k(int n) {
    List<String> list = new ArrayList<>();
    for (int i = 1; i <= n; i++) {
      for (int j = i+1; j <= n; j++) {
        if (
          (i % 4 == 0 && j % 4 == 2) ||
          (i % 4 == 0 && j % 4 == 3) ||
          (i % 4 == 1 && j % 4 == 2) ||
          (i % 4 == 1 && j % 4 == 3) ||
          (i % 4 == 2 && j % 4 == 0) ||
          (i % 4 == 2 && j % 4 == 1) ||
          (i % 4 == 3 && j % 4 == 0) ||
          (i % 4 == 3 && j % 4 == 1)
        ) {
          list.add(String.format("%d %d", i, j));
        }
      }
    }
    return list;
  }
  
  private static List<String> solve4k3(int n) {
    List<String> list = new ArrayList<>();
    for (int i = 1; i <= n; i++) {
      for (int j = i+1; j <= n; j++) {
        if (
          (i % 4 == 0 && j % 4 == 1) ||
          (i % 4 == 0 && j % 4 == 2) ||
          (i % 4 == 1 && j % 4 == 0) ||
          (i % 4 == 1 && j % 4 == 3) ||
          (i % 4 == 2 && j % 4 == 0) ||
          (i % 4 == 2 && j % 4 == 3) ||
          (i % 4 == 3 && j % 4 == 1) ||
          (i % 4 == 3 && j % 4 == 2)
        ) {
          list.add(String.format("%d %d", i, j));
        }
       }
    }
    return list;
  }
  
  private static List<String> solve(int n) {
    switch(n % 4) {
      case 0:
        return solve4k(n);
      case 1:
        return solve4k1(n);
      case 2:
        return solve4k2(n);
      case 3:
        return solve4k3(n);
    }
    return null;
  }
  
  private static void execute(ContestReader reader, PrintWriter out) {
    int n = reader.nextInt();
    List<String> answers = solve(n);
    out.println(answers.size());
    for (String line : answers) {
      out.println(line);
    }
  }
  
  public static void main(String[] args) {
    ContestReader reader = new ContestReader(System.in);
    PrintWriter out = new PrintWriter(System.out);
    execute(reader, out);
    out.flush();
  }
}

class ContestReader {
  private BufferedReader reader;
  private StringTokenizer tokenizer;
  
  ContestReader(InputStream in) {
    reader = new BufferedReader(new InputStreamReader(in));
  }
  
  public String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }
  
  public int nextInt() {
    return Integer.parseInt(next());
  }
  
  public long nextLong() {
    return Long.parseLong(next());
  }
  
  public double nextDouble() {
    return Double.parseDouble(next());
  }
  
  public String[] nextArray(int n) {
    String[] array = new String[n];
    for (int i = 0; i < n; i++) {
      array[i] = next();
    }
    return array;
  }
  
  public int[] nextIntArray(int n) {
    int[] array = new int[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextInt();
    }
    return array;
  }
  
  public long[] nextLongArray(int n) {
    long[] array = new long[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextLong();
    }
    return array;
  }
  
  public double[] nextDoubleArray(int n) {
    double[] array = new double[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextDouble();
    }
    return array;
  }
  
  public 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;
  }
  
  public 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;
  }
  
  public 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;
  }
}

class ModCalculator {
  private final long mod;
  private final ModCombinationCache modCombinationCache;
  
  ModCalculator(long mod) {
    this.mod = mod;
    this.modCombinationCache = new ModCombinationCache();
  }
  
  public long add(long a, long b) {
    return (a + b) % mod;
  }
  
  public long sub(long a, long b) {
    return (a - b + mod) % mod;
  }
  
  public long mul(long a, long b) {
    return (a * b) % mod;
  }
  
  public long pow(long a, long b) {
    if (b == 0) {
      return 1;
    }
    long v = pow(mul(a, a), b / 2);
    if (b % 2 == 1) {
      return mul(v, a);
    } else {
      return v;
    }
  }
  
  public long inverse(long a) {
    return pow(a, mod - 2);
  }
  
  public long div(long a, long b) {
    return mul(a, inverse(b));
  }
  
  public long getF(int n) {
    return modCombinationCache.getF(n);
  }
  
  public long getP(int n, int r) {
    return modCombinationCache.getP(n, r);
  }
  
  public long getC(int n, int k) {
    return modCombinationCache.getC(n, k);
  }
  
  class ModCombinationCache {
    private final List<Long> factorialCache;
    private final List<Long> factorialInverseCache;
    
    public ModCombinationCache() {
      factorialCache = new ArrayList<>();
      factorialCache.add(1L);
      factorialInverseCache = new ArrayList<>();
      factorialInverseCache.add(1L);
    }
    
    private void resize(int n) {
      for (int i = factorialCache.size() - 1; i < n; i++) {
        long v = mul(factorialCache.get(i), i + 1);
        factorialCache.add(v);
        factorialInverseCache.add(inverse(v));
      }
    }
    
    long getF(int n) {
      resize(n);
      return factorialCache.get(n);
    }
    
    long getP(int n, int r) {
      resize(n);
      return mul(factorialCache.get(n), factorialInverseCache.get(n - r));
    }
    
    long getC(int n, int k) {
      resize(n);
      return mul(factorialCache.get(n), mul(factorialInverseCache.get(k), factorialInverseCache.get(n-k)));
    }
  }
}
 
class Algorithm {
  private static void swap(Object[] list, int a, int b) {
    Object tmp = list[a];
    list[a] = list[b];
    list[b] = tmp;
  }
  
  public static <T extends Comparable<? super T>> boolean nextPermutation(T[] ts) {
    int rightMostAscendingOrderIndex = ts.length - 2;
    while (rightMostAscendingOrderIndex >= 0 &&
        ts[rightMostAscendingOrderIndex].compareTo(ts[rightMostAscendingOrderIndex + 1]) >= 0) {
      rightMostAscendingOrderIndex--;
    }
    if (rightMostAscendingOrderIndex < 0) {
      return false;
    }
    
    int rightMostGreatorIndex = ts.length - 1;
    while (ts[rightMostAscendingOrderIndex].compareTo(ts[rightMostGreatorIndex]) >= 0) {
      rightMostGreatorIndex--;
    }
    
    swap(ts, rightMostAscendingOrderIndex, rightMostGreatorIndex);
    for (int i = 0; i < (ts.length - rightMostAscendingOrderIndex - 1) / 2; i++) {
      swap(ts, rightMostAscendingOrderIndex + 1 + i, ts.length - 1 - i);
    }
    return true;
  }
  
  public static void shuffle(int[] array) {
    Random random = new Random();
    int n = array.length;
    for (int i = 0; i < n; i++) {
      int randomIndex = i + random.nextInt(n - i);
      
      int temp = array[i];
      array[i] = array[randomIndex];
      array[randomIndex] = temp;
    }
  }
  
  public static void shuffle(long[] array) {
    Random random = new Random();
    int n = array.length;
    for (int i = 0; i < n; i++) {
      int randomIndex = i + random.nextInt(n - i);
      
      long temp = array[i];
      array[i] = array[randomIndex];
      array[randomIndex] = temp;
    }
  }
  
  public static void sort(int[] array) {
    shuffle(array);
    Arrays.sort(array);
  }
  
  public static void sort(long[] array) {
    shuffle(array);
    Arrays.sort(array);
  }
}

class UnionFind {
  int[] parents;
  int[] ranks;

  UnionFind(int n) {
    parents = new int[n];
    ranks = new int[n];

    for (int i = 0; i < n; i++) {
      parents[i] = i;
    }
  }

  public int getRoot(int index) {
    if (parents[index] == index) {
      return index;
    } else {
      parents[index] = getRoot(parents[index]);
      return parents[index];
    }
  }

  public boolean sameGroup(int a, int b) {
    return getRoot(a) == getRoot(b);
  }

  public void merge(int a, int b) {
    int rootA = getRoot(a);
    int rootB = getRoot(b);
    if (rootA == rootB) {
      return;
    }
    if (ranks[rootA] < ranks[rootB]) {
      parents[rootA] = rootB;
    } else if (ranks[rootB] < ranks[rootA]) {
      parents[rootB] = rootA;
    } else {
      parents[rootA] = rootB;
      ranks[rootB]++;
    }
  }
}
