Problem:
Score : 900 points

Problem Statement

In the city of Nevermore, there are 10^8 streets and 10^8 avenues, both numbered from 0 to 10^8-1.
All streets run straight from west to east, and all avenues run straight from south to north.
The distance between neighboring streets and between neighboring avenues is exactly 100 meters.

Every street intersects every avenue. Every intersection can be described by pair (x, y), where x is avenue ID and y is street ID.

There are N fountains in the city, situated at intersections (X_i, Y_i).
Unlike normal intersections, there's a circle with radius 10 meters centered at the intersection, and there are no road parts inside this circle.

The picture below shows an example of how a part of the city with roads and fountains may look like.

City governors don't like encountering more than one fountain while moving along the same road.
Therefore, every street contains at most one fountain on it, as well as every avenue.

Citizens can move along streets, avenues and fountain perimeters.
What is the shortest distance one needs to cover in order to get from intersection (x_1, y_1) to intersection (x_2, y_2)?

Constraints

0 \leq x_1, y_1, x_2, y_2 < 10^8

1 \leq N \leq 200,000

0 \leq X_i, Y_i < 10^8

X_i \neq X_j for i \neq j

Y_i \neq Y_j for i \neq j

Intersections (x_1, y_1) and (x_2, y_2) are different and don't contain fountains.

All input values are integers.

Input

Input is given from Standard Input in the following format:

x_1 y_1 x_2 y_2
N
X_1 Y_1
X_2 Y_2
:
X_N Y_N

Output

Print the shortest possible distance one needs to cover in order to get from intersection (x_1, y_1) to intersection (x_2, y_2), in meters.
Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-11}.

Sample Input 1

1 1 6 5
3
3 2
5 3
2 4

Sample Output 1

891.415926535897938

One possible shortest path is shown on the picture below. The path starts at the blue point, finishes at the purple point and follows along the red line.

Sample Input 2

3 5 6 4
3
3 2
5 3
2 4

Sample Output 2

400.000000000000000

Sample Input 3

4 2 2 2
3
3 2
5 3
2 4

Sample Output 3

211.415926535897938

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.TreeMap;
import java.util.TreeSet;

public class Main {
	//噴水通過180度
	final double FH = 10 * Math.PI - 20;
	//噴水通過90度
	final double FQ = 5 * Math.PI - 20;

	public static long l=0,l2=0;
	public static void main(String[] args) throws IOException {
		l = System.currentTimeMillis();
		new Main().exec();
		l2 = System.currentTimeMillis();
		
	}

	public void exec() throws IOException {
		
		InputUtil in = new InputUtil();
		PrintWriter out = new PrintWriter(System.out);
		int x1 = (int)in.nextInt();
		int y1 = (int)in.nextInt();
		int x2 = (int)in.nextInt();
		int y2 = (int)in.nextInt();
		int N = (int)in.nextInt();
		int dx = (x2 - x1>0)?1:-1;
		int dy = (y2 - y1>0)?1:-1;
		TreeMap<Integer,Integer> FXMap = new TreeMap<>();
		for(int i=0; i<N; i++) {
			int fx = in.nextInt();
			int fy = in.nextInt();
			if(checkBetween(x1,x2,fx) && checkBetween(y1,y2,fy)) {
				FXMap.put(fx,fy);
			}
		}
		TreeMap<Integer,Integer> FYMap = new TreeMap<>();
		Integer key = null;
		int max = 0;
		while((key = nextEntry(FXMap,key,-dx)) != null){
			int count = 1;
			int y = FXMap.get(key);
			Integer nextY = nextEntry(FYMap,y,dy);
			if(nextY != null) {
				count += FYMap.get(nextY);
			}
			FYMap.put(y,count);
			max = Math.max(max, count);
		}
		
		long base_dir = (x2-x1)*dx + (y2-y1)*dy;
		base_dir *= 100;
		double gosa = 0;
		if(x1==x2 || y1==y2){
			gosa += FH * max;
		} else {
			gosa += FQ * max;
		}
		base_dir += (int)gosa;
		gosa -= (int)gosa;
		StringBuilder sb = new StringBuilder();
		sb.append(base_dir);
		sb.append(".");
		String gosaStr = String.valueOf(gosa);
		sb.append(gosaStr.substring(gosaStr.indexOf(".")+1));
		out.println(sb.toString());
		out.flush();
	}
	
	Integer nextEntry(TreeMap<Integer,Integer> FXMap, Integer key, int dir) {
		if(FXMap.isEmpty())
			return null;
		else if(dir == 1){
			if(key == null)
				return FXMap.firstKey();
			else  
				return FXMap.ceilingKey(key+1);
		}else{
			if(key == null)
				return FXMap.lastKey();
			else  
				return FXMap.floorKey(key-1);
		}
	}
	
	boolean checkBetween(int v1, int v2, int vc) {
		if(v1==v2){
			return v1==vc;
		}else if(v1>v2) {
			return (v2 <= vc && vc <= v1);
		} else {
			return (v1 <= vc && vc <= v2);
		}
	}
	
}




class InputUtil {
	//Static Fields
	private static final int BUFSIZ = 100000;
	
	//Fields
	protected InputStream in;
	private char[] buf = null;
	private int ptr = 0;
	private int max = -1;
	private BufferedReader br = null;
	
	//Constructors
	public InputUtil() {this(System.in,BUFSIZ);}
	public InputUtil(InputStream in, int bufsiz) {
		initBuf(bufsiz);
		initIn(in);
	}
	
	//Methods
	//Initializer
	protected void initIn(InputStream in) {br = new BufferedReader(new InputStreamReader(this.in = in));}
	protected void initBuf(int bufsiz) {buf = new char[bufsiz];}
	
	//buffer operation
	private void next() throws IOException {ptr++; readBuf();}
	private void readBuf() throws IOException {
		if(ptr >= max && br.ready()) {
			if(max>0) Arrays.fill(buf,0,max,(char)0);
			max = br.read(buf);
			ptr = 0;
		}
	}
	
	//Number Input Reader/Parser
	private boolean isNum(char b) {return '0' <= b && b <= '9'; }
	private boolean isMinus(char b) {return b=='-'; }

	private int _nextInt() throws IOException {
		int sign = 1;
		int res = 0;
		char c;
		while (!isNum(c=buf[ptr]) && !isMinus(c)) 
			next();
		if (isMinus(buf[ptr])) {
			sign = -1;
			next();
		}
		while (isNum(c=buf[ptr])) {
			res *= 10;
			res += c - '0' ;
			next();
		}
		next();
		return sign * res;
	}
	
	public int nextInt() throws IOException {
		readBuf();
		return _nextInt();
	}

	public int[] nextInt(int[] result) throws IOException {
		readBuf();
		for(int i=0; i<result.length; i++) {
			result[i] = _nextInt();
		}
		return result;
	}
	
	//Close 
	public void close() throws IOException {
		if(!this.in.equals(System.in)) 
			this.in.close();
	}

}