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

public class C_1368 {
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		
		int n = sc.nextInt();
		int ct = 0;
		ArrayList<Pair> list = new ArrayList<>();
		
		for(int i = 0; i < 2 * n + 1; i++) {
			list.add(new Pair(5, 5 + i));
			ct++;
		}
		
		if(n % 2 == 0) {
			for(int j = 6; j < 5 + 2 * n + 1; j += 4) {
				list.add(new Pair(4, j));
				list.add(new Pair(3, j));
				list.add(new Pair(3, j + 1));
				list.add(new Pair(3, j + 2));
				list.add(new Pair(4, j + 2));
				ct += 5;
				
				list.add(new Pair(6, j));
				list.add(new Pair(7, j));
				list.add(new Pair(7, j + 1));
				list.add(new Pair(7, j + 2));
				list.add(new Pair(6, j + 2));
				ct += 5;
			}
			
			int j = 5 + 2 * n + 1;
			list.add(new Pair(5, j));
			list.add(new Pair(6, j));
			list.add(new Pair(7, j));
			list.add(new Pair(8, j));
			list.add(new Pair(9, j));
			ct += 5;
			while(j > 4) {
				j--;
				list.add(new Pair(9, j));
				ct++;
			}
			list.add(new Pair(8, 4));
			list.add(new Pair(7, 4));
			list.add(new Pair(6, 4));
			list.add(new Pair(5, 4));
			ct += 4;
			
		} else {
			for(int j = 6; j < 5 + 2 * n - 1; j += 4) {
				list.add(new Pair(4, j));
				list.add(new Pair(3, j));
				list.add(new Pair(3, j + 1));
				list.add(new Pair(3, j + 2));
				list.add(new Pair(4, j + 2));
				ct += 5;
				
				list.add(new Pair(6, j));
				list.add(new Pair(7, j));
				list.add(new Pair(7, j + 1));
				list.add(new Pair(7, j + 2));
				list.add(new Pair(6, j + 2));
				ct += 5;
			}
			
			int j = 4 + 2 * n;
			list.add(new Pair(4, j));
			list.add(new Pair(3, j));
			list.add(new Pair(3, j + 1));
			list.add(new Pair(3, j + 2));
			list.add(new Pair(4, j + 2));
			list.add(new Pair(5, j + 2));
			ct += 6;
			
			list.add(new Pair(6, j));
			list.add(new Pair(7, j));
			list.add(new Pair(8, j));
			list.add(new Pair(9, j));
			ct += 4;
			while(j > 4) {
				j--;
				list.add(new Pair(9, j));
				ct++;
			}
			list.add(new Pair(8, 4));
			list.add(new Pair(7, 4));
			list.add(new Pair(6, 4));
			list.add(new Pair(5, 4));
			ct += 4;
		}
		
		pw.println(list.size());
		for(Pair p : list)
			pw.println(p);
		pw.flush();
	}
	
	public static class Pair {
		int i, j;
		
		public Pair(int i, int j) {
			this.i = i;
			this.j = j;
		}
		
		public String toString() {
			return j + " " + i;
		}
	}

	public static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

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

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

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

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

		public int[] nextIntArray(int n) throws IOException {
			int[] array = new int[n];
			for (int i = 0; i < n; i++)
				array[i] = nextInt();
			return array;
		}

		public Integer[] nextIntegerArray(int n) throws IOException {
			Integer[] array = new Integer[n];
			for (int i = 0; i < n; i++)
				array[i] = new Integer(nextInt());
			return array;
		}

		public long[] nextLongArray(int n) throws IOException {
			long[] array = new long[n];
			for (int i = 0; i < n; i++)
				array[i] = nextLong();
			return array;
		}

		public double[] nextDoubleArray(int n) throws IOException {
			double[] array = new double[n];
			for (int i = 0; i < n; i++)
				array[i] = nextDouble();
			return array;
		}

		public static int[] shuffle(int[] a) {
			int n = a.length;
			Random rand = new Random();
			for (int i = 0; i < n; i++) {
				int tmpIdx = rand.nextInt(n);
				int tmp = a[i];
				a[i] = a[tmpIdx];
				a[tmpIdx] = tmp;
			}
			return a;
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}