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.*;
import java.util.*;
import java.math.*; // for bigInteger

public class practice {   

	final private static int M = (int)1e9+7;
	
  	public static void main(String args[]) throws Exception {
        //Faster Output...
        //scanner scan = new scanner(system.in);
        //scan.usedelimiter("");  // for reading character by character
        final PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        final StringBuilder sb = new StringBuilder();
		
		int n = scan.nextInt();
		Pair<Integer,Integer>[] ans = new Pair[4+3*n];
		out.println(4+3*n);
		int ansPointer=0;
		ans[ansPointer++]=new Pair(0,0);
		ans[ansPointer++]=new Pair(0,1);
		ans[ansPointer++]=new Pair(1,0);
		ans[ansPointer++]=new Pair(1,1);
		Pair<Integer,Integer> cur = ans[ansPointer-1];
		while(n-->0) {
			ans[ansPointer++]=new Pair(cur.first,cur.second+1);
			ans[ansPointer++]=new Pair(cur.first+1,cur.second);
			ans[ansPointer++]=new Pair(cur.first+1,cur.second+1);
			cur = ans[ansPointer-1];	
		}
		for(Pair<Integer,Integer> p : ans) {
			sb.append(p.first + " " + p.second + "\n");
		}
		out.println(sb);	

        scan.close();
        out.close();
    }

    private static InputReader scan = new InputReader(System.in);

	static class Pair<T,V> {
		Pair(final T first,final V second) {
			this.first = first;
			this.second = second;
		}
		T first ;
		V second;
    }

    static class InputReader {

        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar;
        private int snumChars;
        private SpaceCharFilter filter;

        public InputReader(final InputStream stream) {
            this.stream = stream;
        }

        public int snext() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }

            int res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));

            return res * sgn;
        }

        public long nextLong() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }

            long res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));

            return res * sgn;
        }

        public String next() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
        
        public void close() throws IOException {
            if(stream==null) {
                return;
            }
            stream.close();
        }
    }

    public static void debug(final int[] ...var) {
        for(final int[] row : var) {
            debug(row);
        }
    }

    public static void debug(final long[] ...var) {
        for(final long[] row : var) {
            debug(row);
        }
    }

    public static void debug(final String[] ...var) {
        for(final String[] row : var) {
            debug(row);
        }
    }

    public static void debug(final double[] ...var) {
        for(final double[] row : var) {
            debug(row);
        }
    }

    public static void debug(final char[] ...var) {
        for(final char[] row : var) {
            debug(row);
        }
    }

    public static void debug(final int ...var) {
        for(final int i:var)  System.err.print(i+" ");
        System.err.println();
    }
    public static void debug(final String ...var) {
        for(final String i:var)  System.err.print(i+" ");
        System.err.println();
    }
    public static void debug(final double ...var) {
        for(final double i:var)  System.err.print(i+" ");
        System.err.println();
    }
    
    public static void debug(final long ...var) {
        for(final long i:var)  System.err.print(i+" ");
        System.err.println();
    }
    
    public static void debug(final char ...var) {
        for(final char c:var)  System.err.print(c+" ");
        System.err.println();
    }

    /*
    public static <T> void debug(T ...varargs) {
        // Warning
        // Heap Pollution might occur
        // this overrides even 1d and 2d array methods as it is an object... 
        // + i am not using object based array like Integer[]
        // I am using int[] so that is a problem as i need Wrapper class as an argument
        for(T val:varargs)  System.err.printf("%s ",val);
        System.err.println();
    }
    */
}