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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Set;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		FastScanner in = new FastScanner(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		ProblemC solver = new ProblemC();
		solver.solve(1, in, out);
		out.close();
	}

	static class ProblemC {
		public void solve(int testNumber, FastScanner in, PrintWriter out) {
			int x1 = in.nextInt();
			int y1 = in.nextInt();
			int x2 = in.nextInt();
			int y2 = in.nextInt();
			int n = in.nextInt();
			int[] x = new int[n];
			int[] y = new int[n];
			for (int i = 0; i < n; i++) {
				x[i] = in.nextInt();
				y[i] = in.nextInt();
			}
			if (x1 > x2) {
				x1 = -x1;
				x2 = -x2;
				for (int i = 0; i < n; i++) {
					x[i] = -x[i];
				}
			}
			if (y1 > y2) {
				y1 = -y1;
				y2 = -y2;
				for (int i = 0; i < n; i++) {
					y[i] = -y[i];
				}
			}

			double ans = 100 * (x2 - x1 + y2 - y1);
			if (x1 == x2) {
				for (int i = 0; i < n; i++) {
					if (x[i] == x1 && y[i] >= y1 && y[i] <= y2) {
						ans -= 20;
						ans += Math.PI * 10;
					}
				}
			} else if (y1 == y2) {
				for (int i = 0; i < n; i++) {
					if (y[i] == y1 && x[i] >= x1 && x[i] <= x2) {
						ans -= 20;
						ans += Math.PI * 10;
					}
				}
			} else {
				List<Point> ps = new ArrayList<>();
				ps.add(new Point(x2, y2));
				for (int i = 0; i < n; i++) {
					if (x[i] >= x1 && x[i] <= x2 && y[i] >= y1 && y[i] <= y2) {
						ps.add(new Point(x[i], y[i]));
					}
				}
				Collections.sort(ps);
				Set<Integer> xs = new HashSet<>();
				for (Point p : ps) {
					xs.add(p.x);
				}
				int[] interestingX = new int[xs.size()];
				int ptr = 0;
				for (int cx : xs) {
					interestingX[ptr++] = cx;
				}
				Arrays.sort(interestingX);
				int[] d = new int[ps.size()];
				IntervalTree tree = new IntervalTree(xs.size());
				for (int i = 0; i < d.length; i++) {
					int id = Arrays.binarySearch(interestingX, ps.get(i).x);
					d[i] = 1 + tree.getMax(0, id);
					tree.set(id, d[i]);
				}
				int c = d[d.length - 1] - 1;
				ans -= c * 20;
				ans += c * Math.PI * 5;
			}
			out.printf("%.15f\n", ans);
		}

		class Point implements Comparable<Point> {
			int x;
			int y;

			Point(int x, int y) {
				this.x = x;
				this.y = y;
			}

			public int compareTo(Point o) {
				if (x != o.x) {
					return x - o.x;
				}
				if (y != o.y) {
					return y - o.y;
				}
				return 0;
			}

		}

		class IntervalTree {
			int[] max;
			int n;

			IntervalTree(int n) {
				this.n = n;
				max = new int[4 * n];
			}

			void set(int pos, int val) {
				set(0, pos, 0, n - 1, val);
			}

			int getMax(int l, int r) {
				return get(0, l, r, 0, n - 1);
			}

			private void set(int root, int pos, int L, int R, int val) {
				if (pos < L || pos > R) {
					return;
				}
				if (pos == L) {
					max[root] = val;
					return;
				}
				int M = (L + R) / 2;
				set(2 * root + 1, pos, L, M, val);
				set(2 * root + 2, pos, M + 1, R, val);
				max[root] = Math.max(max[2 * root + 1], max[2 * root + 2]);
			}

			private int get(int root, int l, int r, int L, int R) {
				if (l > r || l > R || L > r || L > R) {
					return 0;
				}
				if (l == L && r == R) {
					return max[root];
				}
				int M = (L + R) / 2;
				int res = 0;
				res = Math.max(res, get(2 * root + 1, l, Math.min(r, M), L, M));
				res = Math.max(res, get(2 * root + 2, Math.max(l, M + 1), r, M + 1, R));
				return res;
			}

		}

	}

	static class FastScanner {
		private BufferedReader in;
		private StringTokenizer st;

		public FastScanner(InputStream stream) {
			in = new BufferedReader(new InputStreamReader(stream));
		}

		public String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(in.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return st.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

	}
}