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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;

public class _globalRound8 {

	static Reader r = new Reader();
	static PrintWriter out = new PrintWriter(System.out);

	private static void solve1() throws IOException {

		int t = r.nextInt();
		StringBuilder res = new StringBuilder();

		while (t-- > 0) {

			int a = r.nextInt();
			int b = r.nextInt();
			int n = r.nextInt();

			int cnt = 0;
			while (a <= n && b <= n) {
				if (a < b) {
					cnt++;
					a += b;
				} else {
					b += a;
					cnt++;
				}
			}

			res.append(cnt).append("\n");
		}

		out.print(res);
		out.close();
	}

	private static void solve2() throws IOException {

		long k = r.nextLong();

		char str[] = "codeforces".toCharArray();

		// representing k as a sum of values of arr
		long arr[] = new long[10];
		Arrays.fill(arr, 1);

		long num_till_now = 1;
		for (int i = 0; num_till_now < k; i = (i + 1) % 10) {
			num_till_now /= arr[i]++;
			num_till_now *= arr[i];
		}

		StringBuilder ans = new StringBuilder();
		for (int i = 0; i < 10; i++) {
			for (int j = 1; j <= arr[i]; j++) {
				ans.append(str[i]);
			}
		}

		out.print(ans);
		out.close();

	}

	static class Pair {
		int fi, se;

		public Pair(int one, int two) {
			fi = one;
			se = two;
		}
	}

	private static void solve3() throws IOException {

		StringBuilder res = new StringBuilder();

		int n = r.nextInt();

		ArrayList<Pair> vertices = new ArrayList<>();
		vertices.add(new Pair(0, 0));
		vertices.add(new Pair(0, 1));
		vertices.add(new Pair(1, 0));
		vertices.add(new Pair(1, 1));

		while (n-- > 0) {
			int x = vertices.get(vertices.size() - 1).fi;
			int y = vertices.get(vertices.size() - 1).se;
			vertices.add(new Pair(x + 1, y));
			vertices.add(new Pair(x, y + 1));
			vertices.add(new Pair(x + 1, y + 1));
		}

		res.append(vertices.size()).append("\n");
		for (Pair vert : vertices) {
			int x = vert.fi, y = vert.se;
			res.append(x + " " + y).append("\n");
		}

		out.print(res);
		out.close();

	}

	private static void solve4() throws IOException {

		int t = r.nextInt();
		StringBuilder res = new StringBuilder();

		while (t-- > 0) {

			int n = r.nextInt();

			res.append(false).append("\n");
		}

		out.print(res);
		out.close();

	}

	private static void solve5() throws IOException {

		int t = r.nextInt();
		StringBuilder res = new StringBuilder();

		while (t-- > 0) {

			int n = r.nextInt();

			res.append(false).append("\n");
		}

		out.print(res);
		out.close();
	}

	private static void solve6() throws IOException {

		int t = r.nextInt();
		StringBuilder res = new StringBuilder();

		while (t-- > 0) {

			int n = r.nextInt();

			res.append(false).append("\n");
		}

		out.print(res);
		out.close();
	}

	public static void main(String[] args) throws IOException {

//		solve1();

//		solve2();

		solve3();

//		solve4();

//		solve5();

//		solve6();

	}

	static class Reader {

		final private int BUFFER_SIZE = 1 << 12;
		boolean consume = false;
		private byte[] buffer;
		private int bufferPointer, bytesRead;
		private boolean reachedEnd = false;

		public Reader() {
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = 0;
			bytesRead = 0;
		}

		public boolean hasNext() {
			return !reachedEnd;
		}

		private void fillBuffer() throws IOException {
			bytesRead = System.in.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1) {
				buffer[0] = -1;
				reachedEnd = true;
			}
		}

		private void consumeSpaces() throws IOException {
			while (read() <= ' ' && reachedEnd == false)
				;
			bufferPointer--;
		}

		private byte read() throws IOException {
			if (bufferPointer == bytesRead) {
				fillBuffer();
			}
			return buffer[bufferPointer++];
		}

		public String next() throws IOException {
			StringBuilder sb = new StringBuilder();
			consumeSpaces();
			byte c = read();
			do {
				sb.append((char) c);
			} while ((c = read()) > ' ');
			if (consume) {
				consumeSpaces();
			}
			;
			if (sb.length() == 0) {
				return null;
			}
			return sb.toString();
		}

		public String nextLine() throws IOException {
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
			String str = br.readLine();
			return str;
		}

		public int nextInt() throws IOException {
			consumeSpaces();
			int ret = 0;
			byte c = read();
			boolean neg = (c == '-');
			if (neg) {
				c = read();
			}
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');
			if (consume) {
				consumeSpaces();
			}
			if (neg) {
				return -ret;
			}
			return ret;
		}

		public long nextLong() throws IOException {
			consumeSpaces();
			long ret = 0;
			byte c = read();
			boolean neg = (c == '-');
			if (neg) {
				c = read();
			}
			do {
				ret = ret * 10L + c - '0';
			} while ((c = read()) >= '0' && c <= '9');
			if (consume) {
				consumeSpaces();
			}
			if (neg) {
				return -ret;
			}
			return ret;
		}

		public double nextDouble() throws IOException {
			consumeSpaces();
			double ret = 0;
			double div = 1;
			byte c = read();
			boolean neg = (c == '-');
			if (neg) {
				c = read();
			}
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');
			if (c == '.') {
				while ((c = read()) >= '0' && c <= '9') {
					ret += (c - '0') / (div *= 10);
				}
			}
			if (consume) {
				consumeSpaces();
			}
			if (neg) {
				return -ret;
			}
			return ret;
		}

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

		public int[][] nextIntMatrix(int n, int m) throws IOException {
			int[][] grid = new int[n][m];
			for (int i = 0; i < n; i++) {
				grid[i] = nextIntArray(m);
			}
			return grid;
		}

		public char[][] nextCharacterMatrix(int n) throws IOException {
			char[][] a = new char[n][];
			for (int i = 0; i < n; i++) {
				a[i] = next().toCharArray();
			}
			return a;
		}

		public void close() throws IOException {
			if (System.in == null) {
				return;
			} else {
				System.in.close();
			}
		}
	}

}