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
	
		
		    /*
		     * Author- Priyam Vora
		     * BTech 2nd Year DAIICT
		     */
		     
		            
		    import java.io.*;
		    import java.math.*;
	import java.net.NetworkInterface;
	import java.util.*;
		    import javax.print.attribute.SetOfIntegerSyntax;
		     
		    public class CodeMonk_Graph {
		    	private static InputStream stream;
		    	private static byte[] buf = new byte[1024];
		    	private static int curChar;
		    	private static int numChars;
		    	private static SpaceCharFilter filter;
		    	private static PrintWriter pw;
		    	private static long count = 0,mod=1000000007;
		    	private static TreeSet<Integer>ts[]=new TreeSet[200000];
		    	private static HashSet hs=new HashSet();
		     
		    	public static void main(String args[]) throws Exception {
		    		InputReader(System.in);
		    		pw = new PrintWriter(System.out);
		    		//ans();
		    		soln();
		    		pw.close();
		    	}
		     
		    	public static long gcd(long x, long y) {
		    		if (x == 0)
		    			return y;
		    		else
		    			return gcd( y % x,x);
		    	}
		    	
		    	private static int BinarySearch(int a[], int low, int high, int target) {
		    		if (low > high)
		    			return -1;
		    		int mid = low + (high - low) / 2;
		    		if (a[mid] == target)
		    			return mid;
		    		if (a[mid] > target)
		    			high = mid - 1;
		    		if (a[mid] < target)
		    			low = mid + 1;
		    		return BinarySearch(a, low, high, target);
		    	}
		    	
		    	public static String reverseString(String s) {
		    		StringBuilder sb = new StringBuilder(s);
		    		sb.reverse();
		    		return (sb.toString());
		    	}
		    	
		    	public static long pow(long n, long p) {
		    		if(p==0)
		    			return 1;
		    		if(p==1)
		    			return n%mod;
		    		if(p%2==0){
		    			long temp=pow(n, p/2);
		    		return (temp*temp)%mod;
		    		}else{
		    			 	long temp=pow(n,p/2);
		    			 	temp=(temp*temp)%mod;
		    			 	return(temp*n)%mod;
		    			 	
		    		}
		    	}
		     
		    		
		     
		    	public static int[] radixSort(int[] f) {
		    		int[] to = new int[f.length];
		    		{
		    			int[] b = new int[65537];
		    			for (int i = 0; i < f.length; i++)
		    				b[1 + (f[i] & 0xffff)]++;
		    			for (int i = 1; i <= 65536; i++)
		    				b[i] += b[i - 1];
		    			for (int i = 0; i < f.length; i++)
		    				to[b[f[i] & 0xffff]++] = f[i];
		    			int[] d = f;
		    			f = to;
		    			to = d;
		    		}
		    		{
		    			int[] b = new int[65537];
		    			for (int i = 0; i < f.length; i++)
		    				b[1 + (f[i] >>> 16)]++;
		    			for (int i = 1; i <= 65536; i++)
		    				b[i] += b[i - 1];
		    			for (int i = 0; i < f.length; i++)
		    				to[b[f[i] >>> 16]++] = f[i];
		    			int[] d = f;
		    			f = to;
		    			to = d;
		    		}
		    		return f;
		    	}
		     
		    	public static int nextPowerOf2(final int a) {
		    		int b = 1;
		    		while (b < a) {
		    			b = b << 1;
		    		}
		    		return b;
		    	}
		     
		    	public static boolean PointInTriangle(int p1, int p2, int p3, int p4, int p5, int p6, int p7, int p8) {
		    		int s = p2 * p5 - p1 * p6 + (p6 - p2) * p7 + (p1 - p5) * p8;
		    		int t = p1 * p4 - p2 * p3 + (p2 - p4) * p7 + (p3 - p1) * p8;
		     
		    		if ((s < 0) != (t < 0))
		    			return false;
		     
		    		int A = -p4 * p5 + p2 * (p5 - p3) + p1 * (p4 - p6) + p3 * p6;
		    		if (A < 0.0) {
		    			s = -s;
		    			t = -t;
		    			A = -A;
		    		}
		    		return s > 0 && t > 0 && (s + t) <= A;
		    	}
		     
		    	public static float area(int x1, int y1, int x2, int y2, int x3, int y3) {
		    		return (float) Math.abs((x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)) / 2.0);
		    	}
		     
		    	public static boolean isPrime(int n) {
		    		// Corner cases
		    		if (n <= 1)
		    			return false;
		    		if (n <= 3)
		    			return true;
		     
		    		// This is checked so that we can skip 
		    		// middle five numbers in below loop
		    		if (n % 2 == 0 || n % 3 == 0)
		    			return false;
		     
		    		for (int i = 5; i * i <= n; i = i + 6)
		    			if (n % i == 0 || n % (i + 2) == 0)
		    				return false;
		     
		    		return true;
		    	}
		     
		    	//merge Sort
		     
		    	static long sort(int a[])
		    	{  int n=a.length;
		    		int b[]=new int[n];	
		    		return mergeSort(a,b,0,n-1);}
		    	static long mergeSort(int a[],int b[],long left,long right)
		    	{ long c=0;if(left<right)
		    	 {   long mid=left+(right-left)/2;
		    		 c= mergeSort(a,b,left,mid);
		    		 c+=mergeSort(a,b,mid+1,right);
		    		 c+=merge(a,b,left,mid+1,right); }	
		    		return c;	 }
		    	static long merge(int a[],int  b[],long left,long mid,long right)
		    	{long c=0;int i=(int)left;int j=(int)mid; int k=(int)left;
		    	while(i<=(int)mid-1&&j<=(int)right)
		    	{ if(a[i]>a[j]) {b[k++]=a[i++]; }
		    	else	{ b[k++]=a[j++];c+=mid-i;}}
		    	while (i <= (int)mid - 1)   b[k++] = a[i++]; 
		    	while (j <= (int)right) b[k++] = a[j++];
		    	for (i=(int)left; i <= (int)right; i++) 
		    		a[i] = b[i];  return c;  }
		    	public static boolean isSubSequence(String large, String small, int largeLen, int smallLen) {
		    		//base cases
		    		if (largeLen == 0)
		    			return false;
		    		if (smallLen == 0)
		    			return true;
		    		// If last characters of two strings are matching
		    		if (large.charAt(largeLen - 1) == small.charAt(smallLen - 1))
		    			isSubSequence(large, small, largeLen - 1, smallLen - 1);
		    		// If last characters are not matching
		    		return isSubSequence(large, small, largeLen - 1, smallLen);
		    	}
		     
		    	// To Get Input
		    	// Some Buffer Methods
		     
		    	public static void InputReader(InputStream stream1) {
		    		stream = stream1;
		    	}
		     
		    	private static boolean isWhitespace(int c) {
		    		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		    	}
		     
		    	private static boolean isEndOfLine(int c) {
		    		return c == '\n' || c == '\r' || c == -1;
		    	}
		     
		    	private static int read() {
		    		if (numChars == -1)
		    			throw new InputMismatchException();
		    		if (curChar >= numChars) {
		    			curChar = 0;
		    			try {
		    				numChars = stream.read(buf);
		    			} catch (IOException e) {
		    				throw new InputMismatchException();
		    			}
		    			if (numChars <= 0)
		    				return -1;
		    		}
		    		return buf[curChar++];
		    	}
		     
		    	private static int nextInt() {
		    		int c = read();
		    		while (isSpaceChar(c))
		    			c = read();
		    		int sgn = 1;
		    		if (c == '-') {
		    			sgn = -1;
		    			c = read();
		    		}
		    		int res = 0;
		    		do {
		    			if (c < '0' || c > '9')
		    				throw new InputMismatchException();
		    			res *= 10;
		    			res += c - '0';
		    			c = read();
		    		} while (!isSpaceChar(c));
		    		return res * sgn;
		    	}
		     
		    	private static long nextLong() {
		    		int c = read();
		    		while (isSpaceChar(c))
		    			c = read();
		    		int sgn = 1;
		    		if (c == '-') {
		    			sgn = -1;
		    			c = read();
		    		}
		    		long res = 0;
		    		do {
		    			if (c < '0' || c > '9')
		    				throw new InputMismatchException();
		    			res *= 10;
		    			res += c - '0';
		    			c = read();
		    		} while (!isSpaceChar(c));
		    		return res * sgn;
		    	}
		     
		    	private static String nextToken() {
		    		int c = read();
		    		while (isSpaceChar(c))
		    			c = read();
		    		StringBuilder res = new StringBuilder();
		    		do {
		    			res.appendCodePoint(c);
		    			c = read();
		    		} while (!isSpaceChar(c));
		    		return res.toString();
		    	}
		     
		    	private static String nextLine() {
		    		int c = read();
		    		while (isSpaceChar(c))
		    			c = read();
		    		StringBuilder res = new StringBuilder();
		    		do {
		    			res.appendCodePoint(c);
		    			c = read();
		    		} while (!isEndOfLine(c));
		    		return res.toString();
		    	}
		     
		    	private static int[] nextIntArray(int n) {
		    		int[] arr = new int[n];
		    		for (int i = 0; i < n; i++) {
		    			arr[i] = nextInt();
		    		}
		    		return arr;
		    	}
		     
		    	private static int[][] next2dArray(int n, int m) {
		    		int[][] arr = new int[n][m];
		    		for (int i = 0; i < n; i++) {
		    			for (int j = 0; j < m; j++) {
		    				arr[i][j] = nextInt();
		    			}
		    		}
		    		return arr;
		    	}
		    	private static char[][] nextCharArray(int n,int m){
		    		char [][]c=new char[n][m];
		    		for(int i=0;i<n;i++){
		    			String s=nextLine();
		    			for(int j=0;j<s.length();j++){
		    				c[i][j]=s.charAt(j);
		    			}
		    		}
		    		return c;
		    	}
		     
		    	private static long[] nextLongArray(int n) {
		    		long[] arr = new long[n];
		    		for (int i = 0; i < n; i++) {
		    			arr[i] = nextLong();
		    		}
		    		return arr;
		    	}
		     
		    	private static void pArray(int[] arr) {
		    		for (int i = 0; i < arr.length; i++) {
		    			pw.print(arr[i] + " ");
		    		}
		    		pw.println();
		    		return;
		    	}
		     
		    	private static void pArray(long[] arr) {
		    		for (int i = 0; i < arr.length; i++) {
		    			pw.print(arr[i] + " ");
		    		}
		    		pw.println();
		    		return;
		    	}
		     
		    	private static void pArray(boolean[] arr) {
		    		for (int i = 0; i < arr.length; i++) {
		    			pw.print(arr[i] + " ");
		    		}
		    		pw.println();
		    		return;
		    	}
		     
		    	private static boolean isSpaceChar(int c) {
		    		if (filter != null)
		    			return filter.isSpaceChar(c);
		    		return isWhitespace(c);
		    	}
		     
		    	private interface SpaceCharFilter {
		    		public boolean isSpaceChar(int ch);
		    	}
		     
		    	//----------------------------------------My Code------------------------------------------------//
		
	
		    	private static void soln() {
	
		    		
		    		int n=nextInt();
		    	
		    		pw.println((int)(n/2*(Math.ceil((double)n/2))));

		    		for(int i=1;i<=n/2;i++){
		    			for(int j=(n/2)+1;j<=n;j++){
		    				pw.println(i+" "+j);
		    			}
		    		}
		    		
		    		//-----------------------------------------The End--------------------------------------------------------------------------//
		    
		    
		    
		 }
		    	static boolean primeFac(int n){
		    		long c=0;
		    		int flag=1;
		    		HashSet hs=new HashSet();
		    		while(n%2==0){
		    			n=n/2;
		    			flag=0;
		    		
		    		}
		    		if(flag==0)
		    			c++;
		    		flag=1;
		    		for(int i=3;i<=Math.sqrt(n);i+=2){
		    			while(n%i==0){
		    				hs.add(i);
		    				n=n/i;
		    				flag=0;
		    				
		    			}
		    			if(flag==0)
		    				c++;
		    			flag=1;
		    		}
		    		if(n>2){c++;
		    		}
		    		if(c==2){
		    			return true;
		    		}
		    		return false;
		    	}
		    	
		    }
		    
			class Pair implements Comparable<Pair>{
			    long id; 
				long w;
				long h;
				Pair(long id,long w,long h){
					this.id=id;
					if(w>h){
						long temp=w;
						w=h;
						h=temp;
						}
					this.w=w;
					this.h=h;
				}
				@Override
				public int compareTo(Pair o) {
					// TODO Auto-generated method stub
				//	Sort in increasing order
					if(w>o.w){
						return 1;
					}else if(w<o.w){
						return -1;
					}else{
						if(h>o.h)
							return 1;
						else if(h<o.h)
							return -1;
						else
						return 0;
					}
					
					
				}
			
			}
		        class Graph{
		        	private static int V,level[][],count=-1,lev_dfs[],degree=0,no_vert_conn_comp=0;
		        	private Stack <Integer>st=new Stack();
		        	private static LinkedList<Integer > adj[];
		        	private boolean[][] Visite;
		        	private static boolean [] Visited;
		        	private static TreeSet<Integer> ts=new TreeSet();
		        	private static HashMap<String,Integer> hm=new HashMap<>();
		    Graph(int V){
		    V++;
		    this.V=(V);
		    adj=new LinkedList[V];
		    Visite=new boolean[100][100];
	
	 	   Visited=new boolean[V];
		    level=new int[100][100];
		   lev_dfs=new int[V]; 
		   for(int i=0;i<V;i++)
			   adj[i]=new LinkedList<Integer>();
		    }
		     
		    void addEdge(int v,int w,int c){
		    	
		    	if(adj[v]==null){
		    		adj[v]=new LinkedList();
		    	}
		    	adj[v].add(w);
		     String s="";
		     s+=(v+" "+w);
		    hm.put(s, c);	
		    }
		 
		    public static int BFS2(int startVert,int dest){
		    	Visited=new boolean[V];
		    	for(int i=1;i<V;i++){
		    		lev_dfs[i]=-1;
		    	}
		    	Queue<Integer> q=new LinkedList<Integer>();
		    	q.add(startVert);
		    	
		    	lev_dfs[startVert]=0;
		    	while(!q.isEmpty()){
		    		int top=q.poll();
		    		
		    		Iterator<Integer> i= adj[top].listIterator();
		    		while(i.hasNext()){
		    			int n=i.next();
		    			if(!Visited[n]){
		    				q.add(n);
		    				Visited[n]=true;
		    				lev_dfs[n]=lev_dfs[top]+1;
		    			if(n==dest){
		    				q.clear();
		    				return lev_dfs[n];
		    			
		    			}
		    			}
		    		}
		    	}
		    	q.clear();
		    	return -1;
		    }
		    public int getEd(){
		    	return degree/2;
		    }
		    public void get(int from,int to){
		    	int h=lev_dfs[from]-lev_dfs[to];
		    	if(h<=0){
		    		System.out.println(-1);
		    	}else{
		    		System.out.println(h-1);
		    	}
		    }
		    private static boolean check(int x,int y,char c[][]){
			
				if((x>=0 && y>=0) && (x<c.length && y<c[0].length) && c[x][y]!='#'){
					
					return true;
				}
				return false;
			}
		    public int BFS(int x,int y,int k,char[][] c)
		    {
		    	 LinkedList<Pair> queue = new LinkedList<Pair>();
		        //Visited[s]=true;
		   //     queue.add(new Pair(x,y));
		       int count=0;
		   level[x][y]=-1;
		   c[x][y]='M';
		        while (!queue.isEmpty())
		        {
		            Pair temp = queue.poll();
		            //x=temp.idx;
		            //y=temp.val;
		            
		            c[x][y]='M';
		      // System.out.println(x+" "+y+" ---"+count);
		         count++;
		     	if(count==k)
		         {
		         	for(int i=0;i<c.length;i++){
		         		for(int j=0;j<c[0].length;j++){
		         			if(c[i][j]=='M'){
		         				System.out.print(".");
		         			}
		         			else if(c[i][j]=='.')
		         				System.out.print("X");
		         			else
		         				System.out.print(c[i][j]);
		         		}
		         		System.out.println();
		         	}
		         System.exit(0);
		         }
		     	
		         // System.out.println(x+" "+y);
		           // V--;
		           
		        }
		        return V;
		    }
		    
		    private void getAns(int startVertex){
		    	for(int i=0;i<adj[startVertex].size();i++){
		    		int ch=adj[startVertex].get(i);
		    		for(int j=0;j<adj[ch].size();j++){
		    			int ch2=adj[ch].get(j);
		    			if(adj[ch2].contains(startVertex)){
		    				System.out.println(startVertex+" "+ch+" "+ch2);
		    				System.exit(0);
		    			}
		    		}
		    	}
		    }
		    
		     public long dfs(int startVertex){
		    //	 getAns(startVertex);
		    	 long ans=Long.MAX_VALUE;
		    	 //Visited=new boolean[V];
		    	 if(!Visited[startVertex])  {
		    for(int i=0;i<adj[startVertex].size();i++){
		    	 Visited=new boolean[V];
			    	
		    	long t= dfsUtil(adj[startVertex].get(i),Visited);
		    //	System.out.println(t+")))");
			     	ans=Math.min(ans, t);
		    }
		   	//return getAns();
		    	}
		    	 
		    
		     
		    return ans;
		    	}
		 private long dfsUtil(int startVertex, boolean[] Visited) {//0-Blue 1-Pink
		//System.out.println(startVertex);
			 long cost=0;
			// Visited[1]=true;
			// System.out.println(startVertex);
			 String ss="";
			 ss+=(1+" "+startVertex);
		//	System.out.println(hm.get(ss));
			 cost+=hm.get(ss);
			 int c=1;
			 long cout=0;
		      degree=0;
		    	Visited[startVertex]=true;
		    //	lev_dfs[startVertex]=1;
		      st.push(startVertex);
		    while(!st.isEmpty()){
		    	
		    	int top=st.pop();
		    
		   	Iterator<Integer> i=adj[top].listIterator();
		     degree+=adj[top].size();
		    
		    while(i.hasNext()){
		// System.out.println(top+" "+adj[top].size());
		    	int n=i.next();
		 // 	System.out.println(top+" "+n);
		  
		  	if( !Visited[n]){
		    	 if(n==1 && startVertex==top){
		   // 		 System.out.println("---");
		    	 }else{
		    				Visited[n]=true;
		    					st.push(n);
		    				//	System.out.print(n+" ");
		    					lev_dfs[n]=top;
		    					String s="";
		    					s+=(top+" "+n);
		    				//System.out.println(hm.get(s));
		    			cost+=hm.get(s);
		    		 }
		     }
		         }
		//System.out.println("--------------------------------");
		 }
		    	
		    
		    return cost;
			    
		  //  System.out.println("NO");
		   // return c;
		    	
		    
		    
		    
		    }
		        
		        }     
		        	
		        
		    class Dsu{
		    	private int rank[], parent[] ,n;
		    	
		    	Dsu(int size){
		    		this.n=size+1;
		    		rank=new int[n];
		    		parent=new int[n];
		    	makeSet();
		    	}
		    	
		    	void makeSet(){
		    		for(int i=0;i<n;i++){
		    			parent[i]=i;
		    		}
		    	}
		    	
		    	int find(int x){
		    		if(parent[x]!=x){
		    			
		    			parent[x]=find(parent[x]);
		    		}
		    		return parent[x];
		    	}	
		    	
		    	void union(int x,int y){
		    		int xRoot=find(x);
		    		int yRoot=find(y);
		    		
		    		if(xRoot==yRoot)
		    			return;
		    		if(rank[xRoot]<rank[yRoot]){
		    		parent[xRoot]=yRoot;	
		    		}else if(rank[yRoot]<rank[xRoot]){
		    			parent[yRoot]=xRoot;
		    		}else{
		    			parent[yRoot]=xRoot;
		    			rank[xRoot]++;
		    		}
		    		
		    	}
		     
		    }
		    class Heap{
		    	
		    	public static void build_max_heap(long []a,int size){
		    		
		    		for(int i=size/2;i>0;i--){
		    			max_heapify(a, i,size);
		    		}
		    		
		    			}
		    	private static void max_heapify(long[] a,int i,int size){
		    		int left_child=2*i;
		    		int right_child=(2*i+1);
		    		int largest=0;
		    		
		    		if(left_child<size && a[left_child]>a[i]){
		    			largest=left_child;
		    		}else{
		    			largest=i;
		    		}
		    		
		    		if(right_child<size && a[right_child]>a[largest]){
		    			largest=right_child;
		    		}
		    		if(largest!=i){
		    			long temp=a[largest];
		    			a[largest]=a[i];
		    			a[i]=temp;
		    			max_heapify(a, largest,size);
		    		}
		    	}
		    	private static void min_heapify(int[] a,int i){
		    		int left_child=2*i;
		    		int right_child=(2*i+1);
		    		int largest=0;
		    		
		    		if(left_child<a.length && a[left_child]<a[i]){
		    			largest=left_child;
		    		}else{
		    			largest=i;
		    		}
		    		
		    		if(right_child<a.length && a[right_child]<a[largest]){
		    			largest=right_child;
		    		}
		    		if(largest!=i){
		    			int temp=a[largest];
		    			a[largest]=a[i];
		    			a[i]=temp;
		    			min_heapify(a, largest);
		    		}
		    	}
		    	public static void extract_max(int size,long a[]){
		    		if(a.length>1){
		    			long max=a[1];
		    			a[1]=a[a.length-1];
		    			size--;
		    			max_heapify(a, 1,a.length-1);
		    		}
		    	}
		    }
		    
		    class MyComp implements Comparator<Long>{
		        
				@Override
				public int compare(Long o1, Long o2) {
					if(o1<o2){
						return 1;
					}else if(o1>o2){
						return -1;
					}
					return 0;
					
				}
		    }
		    