During a recent research Berland scientists found out that there were n cities in Ancient Berland, joined by two-way paths. Any two cities are joined by no more than one path. No path joins a city with itself. According to a well-known tradition, the road network was built so that it would be impossible to choose three cities from each of which one can get to any other one directly. That is, there was no cycle exactly as long as 3. Unfortunately, the road map has not been preserved till nowadays. Now the scientists are interested how much developed a country Ancient Berland was. Help them - find, what maximal number of roads could be in the country. You also have to restore any of the possible road maps.

Input

The first line contains an integer n (1 ≤ n ≤ 100) — the number of cities in Berland.

Output

On the first line must be printed number m — the maximal number of roads in Berland. Then print m lines containing two numbers each — the numbers of cities that the given road joins. The cities are numbered with integers from 1 to n. If there are several variants of solving the problem, print any of them.

Examples

Input

3


Output

2
1 2
2 3


Input

4


Output

4
1 2
2 3
3 4
4 1
import static java.lang.Math.*;
import java.util.*;
import java.io.*;

public class _test {

    public void solve() throws Exception {

        int n = nextInt();
        println((n*n)/4);
        for (int i=1; i<=n/2; i++)
            for (int j=n/2+1; j<=n; j++)
                println(i,j);
        
    }




    ////////////////////////////////////////////////////////////////////////////

    boolean showDebug = true;

    double EPS = 1e-7;
    int INF = Integer.MAX_VALUE;
    long INFL = Long.MAX_VALUE;
    double INFD = Double.MAX_VALUE;

    int[] dx = {0,1,0,-1};
    int[] dy = {-1,0,1,0};
    int[] dx8 = {0,1,1,1,0,-1,-1,-1};
    int[] dy8 = {-1,-1,0,1,1,1,0,-1};
    int[] knightMovesX = {1,2,2,1,-1,-2,-2,-1};
    int[] knightMovesY = {-2,-1,1,2,2,1,-1,-2};


    @SuppressWarnings("serial")
    class IncMap extends HashMap<Object, Integer> {
        boolean add(Object key, int amount) {
            Integer i = get(key);
            if (i!=null) {
                put(key, i+amount);
                return false;
            } else {
                put(key, amount);
                return true;
            }
        }
        boolean add(Object key) {
            return add(key, 1);
        }
    }


    int min(int... nums) {
        int r = INF;
        for (int i: nums)
            if (i<r) r=i;
        return r;
    }
    int max(int... nums) {
        int r = -INF;
        for (int i: nums)
            if (i>r) r=i;
        return r;
    }
    long minL(long... nums) {
        long r = INFL;
        for (long i: nums)
            if (i<r) r=i;
        return r;
    }
    long maxL(long... nums) {
        long r = -INFL;
        for (long i: nums)
            if (i>r) r=i;
        return r;
    }
    double minD(double... nums) {
        double r = INFD;
        for (double i: nums)
            if (i<r) r=i;
        return r;
    }
    double maxD(double... nums) {
        double r = -INFD;
        for (double i: nums)
            if (i>r) r=i;
        return r;
    }
    long sumArr(int[] arr) {
        long res = 0;
        for (int i: arr)
            res+=i;
        return res;
    }
    long sumArr(long[] arr) {
        long res = 0;
        for (long i: arr)
            res+=i;
        return res;
    }
    double sumArr(double[] arr) {
        double res = 0;
        for (double i: arr)
            res+=i;
        return res;
    }


    long partsFitCnt(long partSize, long wholeSize) {
        return (partSize+wholeSize-1)/partSize;
    }

    boolean odd(long i) {
        return (i&1)==1;
    }

    int digitSum(long i) {
        i = abs(i);
        int r = 0;
        while (i>0) {
            r+=i%10;
            i/=10;
        }
        return r;
    }
    long digitProd(long i) {
        if (i==0) return 0;
        i = abs(i);
        long r = 1;
        while (i>0) {
            r*=i%10;
            i/=10;
        }
        return r;
    }

    long gcd (long a, long b) {
        while (b>0) {
            a%=b;
            a^=b; b^=a; a^=b;
        }
        return a;
    }
    long lcm(long a, long b) {
        return (a*b)/gcd(a,b);
    }

    double log_2 = log(2);
    double log2(double i) {
        return log(i)/log_2;
    }
    long binpow(int x, int n) {
        long r = 1;
        while (n>0) {
            if ((n&1)!=0) r*=x;
            x*=x;
            n>>=1;
        }
        return r;
    }
    long fac(int i) {
        if (i>20) throw new IllegalArgumentException();
        return i<=1 ?  1:fac(i-1)*i;
    }


    double dist(double x, double y, double xx, double yy) {
        return sqrt((xx-x)*(xx-x)+(yy-y)*(yy-y));
    }


    boolean isPalindrome(String s) {
        for (int i=0; i<s.length()/2; i++)
            if (s.charAt(i)!=s.charAt(s.length()-1-i)) return false;
        return true;
    }
    int occurenciesCnt(String s, String pattern) {
        int res = 0;
        for (int i=0; i<s.length()-pattern.length()+1; i++)
            if (s.substring(i, i+pattern.length()).equals(pattern)) res++;
        return res;
    }
    int occurenciesCnt(String s, char pattern) {
        int res = 0;
        for (int i=0; i<s.length(); i++)
            if (s.charAt(i)==pattern) res++;
        return res;
    }


    int[] months = {0,31,28,31,30,31,30,31,31,30,31,30,31};
    boolean isLeapYear(int y) {
        return y%4==0 && (y%400==0 || y%100!=0);
    }
    boolean isValidDate(int d, int m, int y) {
        if (isLeapYear(y) && m==2 && d==29) return true;
        return m>0 && m<=12 && d>0 && d<=months[d];
    }
    int[] nextDay(int d, int m, int y) {
        if (d>=months[m])
            if (m==2 && d==28 && isLeapYear(y)) d++;
            else {d=1; m++;}
        else
            d++;
        if (m==13) {d=1; m=1; y++;}
        return new int[] {d,m,y};
    }

    String str(Object o) {
        return o.toString();
    }


    long timer = System.currentTimeMillis();
    void startTimer() {
        timer = System.currentTimeMillis();
    }
    void stopTimer() {
        System.err.println("time: "+(System.currentTimeMillis()-timer)/1000.0);
    }


    class InputReader {
        byte[] buf = new byte[1<<16];
        int bufPos = 0, bufLim = -1;
        char read() throws IOException {
            if (bufPos>=bufLim) {
                bufLim = System.in.read(buf);
                bufPos = 0;
            }
            return (char)buf[bufPos++];
        }
    }

    InputReader in = new InputReader();
    static BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out), 1<<16);

    char next() throws IOException {
        return in.read();
    }
    char nextChar() throws IOException {
        char c = in.read();
        while (c<=' ') c=in.read();
        return c;
    }
    String nextWord() throws IOException {
        StringBuilder sb = new StringBuilder();
        char c = in.read();
        while (c<=' ') c=in.read();
        while (c>' ') {
            sb.append(c);
            c = in.read();
        }
        return new String(sb);
    }
    String nextLine() throws IOException {
        StringBuilder sb = new StringBuilder();
        char c = in.read();
        while (c<=' ') c=in.read();
        while (c!='\n' && c!='\r') {
            sb.append(c);
            c = in.read();
        }
        return new String(sb);
    }
    int nextInt() throws NumberFormatException, IOException {
        return Integer.parseInt(nextWord());
    }
    long nextLong() throws NumberFormatException, IOException {
        return Long.parseLong(nextWord());
    }
    double nextDouble() throws NumberFormatException, IOException {
        return Double.parseDouble(nextWord());
    }
    int[] nextArr(int size) throws NumberFormatException, IOException {
        int[] arr = new int[size];
        for (int i=0; i<size; i++)
            arr[i] = nextInt();
        return arr;
    }
    long[] nextArrL(int size) throws NumberFormatException, IOException {
        long[] arr = new long[size];
        for (int i=0; i<size; i++)
            arr[i] = nextLong();
        return arr;
    }
    double[] nextArrD(int size) throws NumberFormatException, IOException {
        double[] arr = new double[size];
        for (int i=0; i<size; i++)
            arr[i] = nextDouble();
        return arr;
    }
    String[] nextArrS(int size) throws NumberFormatException, IOException {
        String[] arr = new String[size];
        for (int i=0; i<size; i++)
            arr[i] = nextWord();
        return arr;
    }
    char[] nextArrCh(int size) throws IOException {
        char[] arr = new char[size];
        for (int i=0; i<size; i++)
            arr[i] = nextChar();
        return arr;
    }
    char[][] nextArrCh(int rows, int columns) throws IOException {
        char[][] arr = new char[rows][columns];
        for (int i=0; i<rows; i++)
            for (int j=0; j<columns; j++)
                arr[i][j] = nextChar();
        return arr;
    }

    void print(Object o) throws IOException {
        out.write(o.toString());
    }
    void println(Object o) throws IOException {
        out.write(o.toString());
        out.newLine();
    }
    void print(Object... o) throws IOException {
        for (int i=0; i<o.length; i++) {
            if (i!=0) out.write(' ');
            out.write(o[i].toString());
        }
    }
    void println(Object... o) throws IOException {
        print(o);
        out.newLine();
    }
    void printn(Object o, int n) throws IOException {
        String s = o.toString();
        for (int i=0; i<n; i++) {
            out.write(s);
            if (i!=n-1) out.write(' ');
        }
    }
    void printnln(Object o, int n) throws IOException {
        printn(o, n);
        out.newLine();
    }
    void printArr(int[] arr) throws IOException {
        for (int i=0; i<arr.length; i++) {
            if (i!=0) out.write(' ');
            out.write(Integer.toString(arr[i]));
        }
    }
    void printArr(long[] arr) throws IOException {
        for (int i=0; i<arr.length; i++) {
            if (i!=0) out.write(' ');
            out.write(Long.toString(arr[i]));
        }
    }
    void printArr(double[] arr) throws IOException {
        for (int i=0; i<arr.length; i++) {
            if (i!=0) out.write(' ');
            out.write(Double.toString(arr[i]));
        }
    }
    void printArr(String[] arr) throws IOException {
        for (int i=0; i<arr.length; i++) {
            if (i!=0) out.write(' ');
            out.write(arr[i]);
        }
    }
    void printArr(char[] arr) throws IOException {
        for (char c: arr) out.write(c);
    }
    void printlnArr(int[] arr) throws IOException {
        printArr(arr);
        out.newLine();
    }
    void printlnArr(long[] arr) throws IOException {
        printArr(arr);
        out.newLine();
    }
    void printlnArr(double[] arr) throws IOException {
        printArr(arr);
        out.newLine();
    }
    void printlnArr(String[] arr) throws IOException {
        printArr(arr);
        out.newLine();
    }
    void printlnArr(char[] arr) throws IOException {
        printArr(arr);
        out.newLine();
    }

    void debug(Object... o) {
        if (showDebug) System.err.println(Arrays.deepToString(o));
    }


    public static void main(String[] args) throws Exception {
        Locale.setDefault(Locale.US);
        new _test().solve();
        out.flush(); out.close();
    }
}
