Problem: Leo Jr. draws pictures in his notebook with checkered sheets (that is, each sheet has a regular square grid printed on it). We can assume that the sheets are infinitely large in any direction.

To draw a picture, Leo Jr. colors some of the cells on a sheet gray. He considers the resulting picture beautiful if the following conditions are satisfied:

  * The picture is connected, that is, it is possible to get from any gray cell to any other by following a chain of gray cells, with each pair of adjacent cells in the path being neighbours (that is, sharing a side).
  * Each gray cell has an even number of gray neighbours.
  * There are exactly n gray cells with all gray neighbours. The number of other gray cells can be arbitrary (but reasonable, so that they can all be listed).



Leo Jr. is now struggling to draw a beautiful picture with a particular choice of n. Help him, and provide any example of a beautiful picture.

To output cell coordinates in your answer, assume that the sheet is provided with a Cartesian coordinate system such that one of the cells is chosen to be the origin (0, 0), axes 0x and 0y are orthogonal and parallel to grid lines, and a unit step along any axis in any direction takes you to a neighbouring cell.

Input

The only line contains a single integer n (1 ≤ n ≤ 500) — the number of gray cells with all gray neighbours in a beautiful picture.

Output

In the first line, print a single integer k — the number of gray cells in your picture. For technical reasons, k should not exceed 5 ⋅ 10^5.

Each of the following k lines should contain two integers — coordinates of a gray cell in your picture. All listed cells should be distinct, and the picture should satisdfy all the properties listed above. All coordinates should not exceed 10^9 by absolute value.

One can show that there exists an answer satisfying all requirements with a small enough k.

Example

Input


4


Output


12
1 0
2 0
0 1
1 1
2 1
3 1
0 2
1 2
2 2
3 2
1 3
2 3

Note

The answer for the sample is pictured below:

<image>

Solution (in JAVA):

Solution:
import javafx.util.Pair;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;


public class q_1 {
    static Scanner sc;
    static FastReader fr;
    public static void main(String[] args){
        sc = new Scanner(System.in);
        fr = new FastReader();
        int test = 1;
        for(int tt=0; tt<test; tt++){

            int k = fr.nextInt();
            HashSet<Pair<Integer,Integer>> resultSet = new HashSet<>(100*k);
            if(k==1){
                resultSet.add(new Pair<>(0,0));
                resultSet.add(new Pair<>(-1,0));
                resultSet.add(new Pair<>(1,0));
                resultSet.add(new Pair<>(-1,-1));
                resultSet.add(new Pair<>(0,-1));
                resultSet.add(new Pair<>(0,1));
                resultSet.add(new Pair<>(1,1));
            }
            else {
                int cc = 0;
                int x = 0;
                int y = 0;
                resultSet.add(new Pair<>(-1, 0));
                resultSet.add(new Pair<>(-1, -1));
                resultSet.add(new Pair<>(0, -1));
                while (cc < (k - 1)) {
                    resultSet.add(new Pair<>(x, y));
                    if (cc % 2 == 0) {
                        // go up and down
                        resultSet.add(new Pair<>(x, y + 1));
                        resultSet.add(new Pair<>(x, y + 2));
                        resultSet.add(new Pair<>(x + 1, y + 2));
                        resultSet.add(new Pair<>(x + 2, y + 2));
                        resultSet.add(new Pair<>(x + 2, y + 1));
                        resultSet.add(new Pair<>(x+1,0));
                        x += 2;
                    } else {
                        resultSet.add(new Pair<>(x, y - 1));
                        resultSet.add(new Pair<>(x, y - 2));
                        resultSet.add(new Pair<>(x + 1, y - 2));
                        resultSet.add(new Pair<>(x + 2, y - 2));
                        resultSet.add(new Pair<>(x + 2, y - 1));
                        resultSet.add(new Pair<>(x+1,0));
                        x += 2;
                    }
                    cc++;
                }
                resultSet.add(new Pair<>(x, 0));
                if (k % 2 == 0) {
                    resultSet.add(new Pair<>(x, y - 1));
                    resultSet.add(new Pair<>(x + 1, 0));
                    resultSet.add(new Pair<>(x + 1, -1));
                } else {
                    resultSet.add(new Pair<>(x, 1));
                    resultSet.add(new Pair<>(x + 1, 0));
                    resultSet.add(new Pair<>(x + 1, 1));
                }
            }
            System.out.println(resultSet.size());
            for(Pair p: resultSet){
                System.out.println(p.getKey()+" "+ p.getValue());
            }
        }
    }

    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }

    public static Integer[] getIntArrayFromSingleLine(){
        List<Integer> list = new LinkedList<>();
        String[] str = fr.nextLine().split(" ");
        for(String s: str){
            list.add(Integer.parseInt(s));
        }
        Integer[] arr = new Integer[list.size()];
        return list.toArray(arr);
    }

    public static Long[] getLongArrayFromSingleLine(){
        List<Long> list = new LinkedList<>();
        String[] str = fr.nextLine().split(" ");
        for(String s: str){
            list.add(Long.parseLong(s));
        }
        Long[] longs = new Long[list.size()];
        return list.toArray(longs);
    }

    public static Double[] getDoubleArrayFromSingleLine(){
        List<Double> list = new LinkedList<>();
        String[] str= fr.nextLine().split(" ");
        for(String s: str){
            list.add(Double.parseDouble(s));
        }
        Double[] doubles = new Double[list.size()];
        return list.toArray(doubles);
    }

    public static String[] getStringArrayFromSingleLine(){
        return fr.nextLine().split(" ");
    }

    public static int[] getArray(int n){
        int[] arr = new int[n];
        for(int i=0; i<n; i++){
            arr[i] = fr.nextInt();
        }
        return arr;
    }

    public static long[] getLongArray(int n){
        long[] res = new long[n];
        for(int i=0; i<n; i++){
            res[i] = fr.nextLong();
        }
        return res;
    }

    public static double[] getDoubleArray(int n){
        double[] arr = new double[n];
        for(int i=0; i<n ; i++){
            arr[i] = fr.nextDouble();
        }
        return arr;
    }

    public static char[] getCharArray(){
        return fr.next().toCharArray();
    }

    public static String[] getStringArray(int n){
        String[] strings = new String[n];
        for(int i=0; i<n; i++){
            strings[i] = fr.next();
        }
        return strings;
    }

    // Get GCD
    public static int getGCD(int a, int b){
        return (a==0 ? b : getGCD(b%a, a));
    }

    public static int getGCD(int[] arr){
        int n = arr.length;
        if(n==0){
            return -1;
        }
        int res = arr[0];
        for(int i=1; i<n; i++){
            res = getGCD(res, arr[i]);
        }
        return res;
    }

    // Get all prime numbers till N using seive of Eratosthenes
    public static List<Integer> getPrimesTill(int n){
        boolean[] arr = new boolean[n+1];
        List<Integer> primes = new LinkedList<>();
        for(int i=2; i<=n; i++){
            if(!arr[i]){
                primes.add(i);
                for(long j=(i*i); j<=n; j+=i){
                    arr[(int)j] = true;
                }
            }
        }
        return primes;
    }


    // This method returns list of PrimeFactors of a number in O(sqrt(N));
    public static Map<Integer,Integer> getPrimeFactors(long n){
        Map<Integer,Integer> res = new HashMap<>();
        int sqrt = (int) Math.sqrt(n);
        if(n%2 == 0){
            int c = 0;
            while(n%2==0){
                c++;
                n/=2;
            }
            res.put(2,c);
        }
        for(int i=3; i<=sqrt; i+=2){
            if(n%i == 0) {
                int c = 0;
                while (n % i == 0) {
                    c++;
                    n /= i;
                }
                res.put(i,c);
            }
        }
        if(n!=1){
            res.put((int)n,1);
        }
        return res;
    }

}