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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.List;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.Reader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyInput in = new MyInput(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        BBalancedNeighbors solver = new BBalancedNeighbors();
        solver.solve(1, in, out);
        out.close();
    }

    static class BBalancedNeighbors {
        List<int[]> edges = new ArrayList<>();

        public void solve(int testNumber, MyInput in, PrintWriter out) {
//        test(7);
            int n = in.nextInt();
            if (n % 2 == 0) {
                List<int[]> pair = new ArrayList<>();
                for (int i = 1; i < n + 1 - i; i++) {
                    pair.add(new int[]{i, n + 1 - i});
                }
                for (int j = 0; j < pair.size(); j++) {
                    if (j != 0 || n > 4) {
                        add(pair.get(j)[0], pair.get((j + 1) % pair.size())[0]);
                        add(pair.get(j)[0], pair.get((j + 1) % pair.size())[1]);
                        add(pair.get(j)[1], pair.get((j + 1) % pair.size())[0]);
                        add(pair.get(j)[1], pair.get((j + 1) % pair.size())[1]);
                    }
                }
            } else {
                List<int[]> pair = new ArrayList<>();
                for (int i = 1; i < n - i; i++) {
                    pair.add(new int[]{i, n - i});
                }
                for (int j = 0; j < pair.size() - 1; j++) {
                    add(pair.get(j)[0], pair.get((j + 1) % pair.size())[0]);
                    add(pair.get(j)[0], pair.get((j + 1) % pair.size())[1]);
                    add(pair.get(j)[1], pair.get((j + 1) % pair.size())[0]);
                    add(pair.get(j)[1], pair.get((j + 1) % pair.size())[1]);
                }
                add(pair.get(0)[0], n);
                add(pair.get(0)[1], n);
                if (n > 3) {
                    add(pair.get(pair.size() - 1)[0], n);
                    add(pair.get(pair.size() - 1)[1], n);
                }
            }
            out.println(edges.size());
            for (int[] e : edges) {
                out.println(e[0] + " " + e[1]);
            }
        }

        void add(int i, int j) {
            edges.add(new int[]{i, j});
        }

    }

    static class MyInput {
        private final BufferedReader in;
        private static int pos;
        private static int readLen;
        private static final char[] buffer = new char[1024 * 8];
        private static char[] str = new char[500 * 8 * 2];
        private static boolean[] isDigit = new boolean[256];
        private static boolean[] isSpace = new boolean[256];
        private static boolean[] isLineSep = new boolean[256];

        static {
            for (int i = 0; i < 10; i++) {
                isDigit['0' + i] = true;
            }
            isDigit['-'] = true;
            isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true;
            isLineSep['\r'] = isLineSep['\n'] = true;
        }

        public MyInput(InputStream is) {
            in = new BufferedReader(new InputStreamReader(is));
        }

        public int read() {
            if (pos >= readLen) {
                pos = 0;
                try {
                    readLen = in.read(buffer);
                } catch (IOException e) {
                    throw new RuntimeException();
                }
                if (readLen <= 0) {
                    throw new MyInput.EndOfFileRuntimeException();
                }
            }
            return buffer[pos++];
        }

        public int nextInt() {
            int len = 0;
            str[len++] = nextChar();
            len = reads(len, isSpace);
            int i = 0;
            int ret = 0;
            if (str[0] == '-') {
                i = 1;
            }
            for (; i < len; i++) ret = ret * 10 + str[i] - '0';
            if (str[0] == '-') {
                ret = -ret;
            }
            return ret;
        }

        public char nextChar() {
            while (true) {
                final int c = read();
                if (!isSpace[c]) {
                    return (char) c;
                }
            }
        }

        int reads(int len, boolean[] accept) {
            try {
                while (true) {
                    final int c = read();
                    if (accept[c]) {
                        break;
                    }
                    if (str.length == len) {
                        char[] rep = new char[str.length * 3 / 2];
                        System.arraycopy(str, 0, rep, 0, str.length);
                        str = rep;
                    }
                    str[len++] = (char) c;
                }
            } catch (MyInput.EndOfFileRuntimeException e) {
            }
            return len;
        }

        static class EndOfFileRuntimeException extends RuntimeException {
        }

    }
}

