Problem: Jzzhu has picked n apples from his big apple tree. All the apples are numbered from 1 to n. Now he wants to sell them to an apple store. 

Jzzhu will pack his apples into groups and then sell them. Each group must contain two apples, and the greatest common divisor of numbers of the apples in each group must be greater than 1. Of course, each apple can be part of at most one group.

Jzzhu wonders how to get the maximum possible number of groups. Can you help him?

Input

A single integer n (1 ≤ n ≤ 105), the number of the apples.

Output

The first line must contain a single integer m, representing the maximum number of groups he can get. Each of the next m lines must contain two integers — the numbers of apples in the current group.

If there are several optimal answers you can print any of them.

Examples

Input

6


Output

2
6 3
2 4


Input

9


Output

3
9 3
2 4
6 8


Input

2


Output

0

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.math.BigInteger;
import static java.lang.Math.*;
 
/* spar5h */
 
public class cf2 implements Runnable {   
	
	class Pair {
		
		int i, j;
		
		Pair(int i, int j) {
			this.i = i;
			this.j = j;
		}
	}
	
	public void run() {
		
		InputReader s = new InputReader(System.in);
		PrintWriter w = new PrintWriter(System.out);
		
		int n = s.nextInt();
		
		int[] spf = new int[n + 1];

		ArrayList<Integer>[] adj = new ArrayList[n + 1];
		
		for(int i = 1; i <= n; i++) {
			spf[i] = i;
			adj[i] = new ArrayList<Integer>();
		}
		
		for(int i = 2; i <= n; i++) {
			
			adj[spf[i]].add(i);
			
			if(spf[i] != i)
				continue;
			
			for(int j = 2; (long)i * j <= n; j++)
				if(spf[i * j] == i * j)
					spf[i * j] = i;
		}
		
		int[] flag = new int[n + 1];
		
		ArrayList<Pair> res = new ArrayList<Pair>();
		
		for(int i = n / 2; i >= 3; i--) {
			
			if(adj[i].size() % 2 == 1) {
				res.add(new Pair(i, 2 * i));
				flag[2 * i] = 1;
			}
			
			for(int j = adj[i].size() % 2; j < adj[i].size(); j+=2)
				res.add(new Pair(adj[i].get(j), adj[i].get(j + 1)));
		}
		
		ArrayList<Integer> two = new ArrayList<Integer>();
		
		if(n > 1) {
			for(int i : adj[2])
				if(flag[i] == 0)
					two.add(i);
		}
		
		for(int i = 0; i + 1 < two.size(); i+=2)
			res.add(new Pair(two.get(i), two.get(i + 1)));
		
		w.println(res.size());
		
		for(int i = 0; i < res.size(); i++)
			w.println(res.get(i).i + " " + res.get(i).j);
		
		w.close();
	}
	
	static class InputReader {
		
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;
		
		public InputReader(InputStream stream) {
			this.stream = stream;
		}
		
		public 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++];
		}
		 
		public String nextLine() {
			
			BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
			String str = "";
	        
			try {
	            str = br.readLine();
	        }
	        catch (IOException e) {
	            e.printStackTrace();
	        }
			
	        return str;
		}
		
		public 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;
		}
		
		public 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;
		}
		
		public double nextDouble() {
			
			int c = read();
			
			while (isSpaceChar(c))
				c = read();
			
			int sgn = 1;
			
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			
			double res = 0;
			
			while (!isSpaceChar(c) && c != '.') {
				
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, nextInt());
				
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				
				res *= 10;
				res += c - '0';
				c = read();
			}
			
			if (c == '.') {
				
				c = read();
				double m = 1;
				while (!isSpaceChar(c)) 
				{
					if (c == 'e' || c == 'E')
						return res * Math.pow(10, nextInt());
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					m /= 10;
					res += (c - '0') * m;
					c = read();
				}
			}
			
			return res * sgn;
		}
		
		public String readString() {
			
			int c = read();
			
			while (isSpaceChar(c))
				c = read();
			
			StringBuilder res = new StringBuilder();
			
			do {
				res.appendCodePoint(c);
				c = read();
			} 
			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 String next() {
			return readString();
		}
		
		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	
	}
 
	public static void main(String args[]) throws Exception {
		new Thread(null, new cf2(),"cf2",1<<26).start();
	}
}