Problem: Girl Lena likes it when everything is in order, and looks for order everywhere. Once she was getting ready for the University and noticed that the room was in a mess — all the objects from her handbag were thrown about the room. Of course, she wanted to put them back into her handbag. The problem is that the girl cannot carry more than two objects at a time, and cannot move the handbag. Also, if he has taken an object, she cannot put it anywhere except her handbag — her inherent sense of order does not let her do so.

You are given the coordinates of the handbag and the coordinates of the objects in some Сartesian coordinate system. It is known that the girl covers the distance between any two objects in the time equal to the squared length of the segment between the points of the objects. It is also known that initially the coordinates of the girl and the handbag are the same. You are asked to find such an order of actions, that the girl can put all the objects back into her handbag in a minimum time period.

Input

The first line of the input file contains the handbag's coordinates xs, ys. The second line contains number n (1 ≤ n ≤ 24) — the amount of objects the girl has. The following n lines contain the objects' coordinates. All the coordinates do not exceed 100 in absolute value. All the given positions are different. All the numbers are integer.

Output

In the first line output the only number — the minimum time the girl needs to put the objects into her handbag. 

In the second line output the possible optimum way for Lena. Each object in the input is described by its index number (from 1 to n), the handbag's point is described by number 0. The path should start and end in the handbag's point. If there are several optimal paths, print any of them. 

Examples

Input

0 0
2
1 1
-1 1


Output

8
0 1 2 0 


Input

1 1
3
4 3
3 4
0 0


Output

32
0 1 2 0 3 0 

Solution (in JAVA):

Solution:


import java.util.*;
import java.io.*;
import java.awt.Point;
import java.math.BigInteger;

import static java.lang.Math.*;

// Solution is at the bottom of code

public class ProblemC_008 implements Runnable{
	
	final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
	
	BufferedReader in;
	OutputWriter out;
	StringTokenizer tok = new StringTokenizer("");
	
	public static void main(String[] args){
		new Thread(null, new ProblemC_008(), "", 128 * (1L << 20)).start();
	}
	
	/////////////////////////////////////////////////////////////////////
	
	void init() throws FileNotFoundException{
		Locale.setDefault(Locale.US);
		
		if (ONLINE_JUDGE){
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new OutputWriter(System.out);
		}else{
			in = new BufferedReader(new FileReader("input.txt"));
			out = new OutputWriter("output.txt");
		}
	}
	
	////////////////////////////////////////////////////////////////
	
	long timeBegin, timeEnd;

	void time(){
		timeEnd = System.currentTimeMillis();
		System.err.println("Time = " + (timeEnd - timeBegin));
	}
	
	void debug(Object... objects){
		if (ONLINE_JUDGE){
			for (Object o: objects){
				System.err.println(o.toString());
			}
		}
	}
	
	/////////////////////////////////////////////////////////////////////
	
	public void run(){
		try{
			timeBegin = System.currentTimeMillis();
			Locale.setDefault(Locale.US);
			
			init();
			solve();
			
			out.close();
			time();
		}catch (Exception e){
			e.printStackTrace(System.err);
			System.exit(-1);
		}
	}
	
	/////////////////////////////////////////////////////////////////////
	
	String delim = " ";
	
	String readString() throws IOException{
		while(!tok.hasMoreTokens()){
			try{
				tok = new StringTokenizer(in.readLine());
			}catch (Exception e){
				return null;
			}
		}
		
		return tok.nextToken(delim);
	}
	
	String readLine() throws IOException{
		return in.readLine();
	}
	
	/////////////////////////////////////////////////////////////////
	
	final char NOT_A_SYMBOL = '\0';
	
	char readChar() throws IOException{
		int intValue = in.read();
		
		if (intValue == -1){
			return NOT_A_SYMBOL;
		}
		
		return (char) intValue;
	}
	
	char[] readCharArray() throws IOException{
		return readLine().toCharArray();
	}
	
	/////////////////////////////////////////////////////////////////
	
	int readInt() throws IOException{
		return Integer.parseInt(readString());
	}
	
	int[] readIntArray(int size) throws IOException{
		int[] array = new int[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readInt();
		}
		
		return array;
	}
	
	///////////////////////////////////////////////////////////////////
	
	long readLong() throws IOException{
		return Long.parseLong(readString());
	}
	
	long[] readLongArray(int size) throws IOException{
		long[] array = new long[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readLong();
		}
		
		return array;
	}
	
	////////////////////////////////////////////////////////////////////
	
	double readDouble() throws IOException{
		return Double.parseDouble(readString());
	}
	
	double[] readDoubleArray(int size) throws IOException{
		double[] array = new double[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readDouble();
		}
		
		return array;
	}
	
	/////////////////////////////////////////////////////////////////////
	
	Point readPoint() throws IOException{
		return new Point(readInt(), readInt());
	}
	
	Point[] readPointArray(int size) throws IOException{
		Point[] array = new Point[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readPoint();
		}
		
		return array;
	}
	
	/////////////////////////////////////////////////////////////////////
	
	class OutputWriter extends PrintWriter{

		final int DEFAULT_PRECISION = 12;
		
		int precision;
		String format, formatWithSpace;
		
		{
			precision = DEFAULT_PRECISION;
			
			format = createFormat(precision);
			formatWithSpace = format + " ";
		}
		
		public OutputWriter(OutputStream out) {
			super(out);
		}

		public OutputWriter(String fileName) throws FileNotFoundException {
			super(fileName);
		}
		
		public int getPrecision() {
			return precision;
		}

		public void setPrecision(int precision) {
			this.precision = precision;
			
			format = createFormat(precision);
			formatWithSpace = format + " ";
		}
		
		private String createFormat(int precision){
			return "%." + precision + "f";
		}
		
		@Override
		public void print(double d){
			printf(format, d);
		}
		
		public void printWithSpace(double d){
			printf(formatWithSpace, d);
		}

		public void printAll(double...d){
			for (int i = 0; i < d.length - 1; ++i){
				printWithSpace(d[i]);
			}
			
			print(d[d.length - 1]);
		}
		
		@Override
		public void println(double d){
			printlnAll(d);
		}
		
		public void printlnAll(double... d){
			printAll(d);
			println();
		}
	}
	
	/////////////////////////////////////////////////////////////////////
	
	int[][] steps = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}}; 
	
	boolean check(int index, int lim){
		return (0 <= index && index < lim);
	}
	
	/////////////////////////////////////////////////////////////////////
	
	void solve() throws IOException{
		Point bag = readPoint();
		
		int n = readInt();
		
		Point[] points = new Point[n];
		
		for (int i = 0; i < n; ++i){
			points[i] = readPoint();
		}
		
		int[] dist = new int[n];
		for (int i = 0; i < n; ++i){
			int dx = points[i].x - bag.x;
			int dy = points[i].y - bag.y;
			
			dist[i] = dx * dx + dy * dy;
		}
		
		int[][] d = new int[n][n];
		for (int i = 0; i < n; ++i){
			for (int j = 0; j < n; ++j){
				int dx = points[i].x - points[j].x;
				int dy = points[i].y - points[j].y;
				
				d[i][j] = dx * dx + dy * dy;
				d[i][j] += dist[i] + dist[j];
			}
		}
		
		int[] singleMasks = new int[n];
		for (int i = 0; i < n; ++i){
			singleMasks[i] = (1 << i);
		}
		
		int[][] doubleMasks = new int[n][n];
		for (int i = 0; i < n; ++i){
			for (int j = 0; j < n; ++j){
				doubleMasks[i][j] = (singleMasks[i] | singleMasks[j]);
			}
		}
		
		int lim = (1 << n);
		int[] dp = new int[lim];
		
		Arrays.fill(dp, Integer.MAX_VALUE);
		dp[0] = 0;
		
		int[] p = new int[lim];
		Arrays.fill(p, -1);
		
		for (int mask = 0; mask < lim; ++mask){
			if (dp[mask] == Integer.MAX_VALUE){
				continue;
			}
			
			int minBit = -1;
			
			for (int bit = 0; bit < n; ++bit){
				if (checkBit(mask, bit)) continue;
				
				if (minBit == -1 || (dist[minBit] > dist[bit])){
					minBit = bit;
				}
			}
			
			if (minBit == -1){
				continue;
			}
			
			for (int bit = 0; bit < n; ++bit){
				if (checkBit(mask, bit)) continue;
				
				int newMask = (mask | (1 << minBit) | (1 << bit));
				
				if (dp[newMask] > dp[mask] + d[minBit][bit]){
					dp[newMask] = dp[mask] + d[minBit][bit];
					p[newMask] = minBit * n + bit;
				}
			}
		}
		
		out.println(dp[lim-1]);
		
		int curMask = lim - 1;
		while (p[curMask] != -1){
			out.print("0 ");
			
			int first = p[curMask] / n;
			int second = p[curMask] % n;
			
			out.print((first + 1) + " ");
			curMask ^= (1 << first);
			
			if (first != second){
				out.print((second + 1) + " ");
				curMask ^= (1 << second);
			}
		}
		
		out.println("0");
	}

	private boolean checkBit(int mask, int bitNumber) {
		return (mask & (1 << bitNumber)) != 0;
	}
	
	boolean checkMask(int mask, int innerMask){
		return (mask & innerMask) == innerMask;
	}
}