Problem:
Score : 900 points

Problem Statement

There are N pinholes on the xy-plane. The i-th pinhole is located at (x_i,y_i).

We will denote the Manhattan distance between the i-th and j-th pinholes as d(i,j)(=|x_i-x_j|+|y_i-y_j|).

You have a peculiar pair of compasses, called Manhattan Compass.
This instrument always points at two of the pinholes.
The two legs of the compass are indistinguishable, thus we do not distinguish the following two states: the state where the compass points at the p-th and q-th pinholes, and the state where it points at the q-th and p-th pinholes.

When the compass points at the p-th and q-th pinholes and d(p,q)=d(p,r), one of the legs can be moved so that the compass will point at the p-th and r-th pinholes.

Initially, the compass points at the a-th and b-th pinholes.
Find the number of the pairs of pinholes that can be pointed by the compass.

Constraints

2≦N≦10^5

1≦x_i, y_i≦10^9

1≦a < b≦N

When i ≠ j, (x_i, y_i) ≠ (x_j, y_j)

x_i and y_i are integers.

Input

The input is given from Standard Input in the following format:

N a b
x_1 y_1
:
x_N y_N

Output

Print the number of the pairs of pinholes that can be pointed by the compass.

Sample Input 1

5 1 2
1 1
4 3
6 1
5 5
4 8

Sample Output 1

4

Initially, the compass points at the first and second pinholes.

Since d(1,2) = d(1,3), the compass can be moved so that it will point at the first and third pinholes.

Since d(1,3) = d(3,4), the compass can also point at the third and fourth pinholes.

Since d(1,2) = d(2,5), the compass can also point at the second and fifth pinholes.

No other pairs of pinholes can be pointed by the compass, thus the answer is 4.

Sample Input 2

6 2 3
1 3
5 3
3 5
8 4
4 7
2 5

Sample Output 2

4

Sample Input 3

8 1 2
1 5
4 3
8 2
4 7
8 8
3 3
6 6
4 8

Sample Output 3

7

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

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Main {

    void solve() throws IOException {
        // 問題を勘違いしてた
        int n = ni();
        int a = ni() - 1;
        int b = ni() - 1;
        long[] x = new long[n];
        long[] y = new long[n];
        for (int i = 0; i < n; i++) {
            long xx = nl();
            long yy = nl();
            x[i] = yy + xx - 2;
            y[i] = yy - xx + 999999999;

            out.println("(" + x[i] + ", " + (y[i] - 999999999) + ")");
        }

        long d = Math.max(Math.abs(x[a] - x[b]), Math.abs(y[a] - y[b]));

        long t = 2000000000;

        TreeSet<Long> setX = new TreeSet<>();
        for (int i = 0; i < n; i++) {
            if (i != a && i != b) {
                setX.add(y[i] * t + x[i]);
            }
        }

        TreeSet<Long> setY = new TreeSet<>();
        for (int i = 0; i < n; i++) {
            if (i != a && i != b) {
                setY.add(x[i] * t + y[i]);
            }
        }

        ArrayDeque<Long> Q = new ArrayDeque<>();
        Q.add(x[a] * t + y[a]);
        Q.add(x[b] * t + y[b]);

        int ans = 0;

        while (!Q.isEmpty()) {
            long p = Q.poll();
            long xx = p / t;
            long yy = p % t;

            out.println("(" + xx + ", " + (yy - 999999999) + ")");
            out.println(setX);
            out.println(setY);
            ans++;

            if (xx + d < t) {
                long sy = Math.max(0, yy - d);
                long ty = Math.min(t - 1, yy + d);
                while (true) {
                    Long r = setY.higher((xx + d) * t + sy - 1);
                    if (r == null || r > (xx + d) * t + ty) break;
                    long rx = r / t;
                    long ry = r % t;
                    Q.add(r);
                    setY.remove(r);
                    setX.remove(ry * t + rx);
                }
            }

            if (xx - d >= 0) {
                long sy = Math.max(0, yy - d);
                long ty = Math.min(t - 1, yy + d);
                while (true) {
                    Long r = setY.higher((xx - d) * t + sy - 1);
                    if (r == null || r > (xx - d) * t + ty) break;
                    long rx = r / t;
                    long ry = r % t;
                    Q.add(r);
                    setY.remove(r);
                    setX.remove(ry * t + rx);
                }
            }

            if (yy + d < t) {
                long sx = Math.max(0, xx - d);
                long tx = Math.min(t - 1, xx + d);
                while (true) {
                    Long r = setX.higher((yy + d) * t + sx - 1);
                    if (r == null || r > (yy + d) * t + tx) break;
                    long ry = r / t;
                    long rx = r % t;
                    Q.add(rx * t + ry);
                    setX.remove(r);
                    setY.remove(rx * t + ry);
                }
            }

            if (yy - d >= 0) {
                long sx = Math.max(0, xx - d);
                long tx = Math.min(t - 1, xx + d);
                while (true) {
                    Long r = setX.higher((yy - d) * t + sx - 1);
                    if (r == null || r > (yy - d) * t + tx) break;
                    long ry = r / t;
                    long rx = r % t;
                    Q.add(rx * t + ry);
                    setX.remove(r);
                    setY.remove(rx * t + ry);
                }
            }
        }

        out.println(ans);
    }

    String ns() throws IOException {
        while (!tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine(), " ");
        }
        return tok.nextToken();
    }

    int ni() throws IOException {
        return Integer.parseInt(ns());
    }

    long nl() throws IOException {
        return Long.parseLong(ns());
    }

    double nd() throws IOException {
        return Double.parseDouble(ns());
    }

    String[] nsa(int n) throws IOException {
        String[] res = new String[n];
        for (int i = 0; i < n; i++) {
            res[i] = ns();
        }
        return res;
    }

    int[] nia(int n) throws IOException {
        int[] res = new int[n];
        for (int i = 0; i < n; i++) {
            res[i] = ni();
        }
        return res;
    }

    long[] nla(int n) throws IOException {
        long[] res = new long[n];
        for (int i = 0; i < n; i++) {
            res[i] = nl();
        }
        return res;
    }

    class INA {
        int[][] a;

        INA(int n, int m) throws IOException {
            this(n, m, -1);
        }

        INA(int n, int m, int t) throws IOException {
            a = new int[m][n];

            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    a[j][i] = ni() + t;
                }
            }
        }

        int[] get(int i) {
            return a[i - 1];
        }
    }

    static BufferedReader in;
    static PrintWriter out;
    static StringTokenizer tok;

    public static void main(String[] args) throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        tok = new StringTokenizer("");
        Main main = new Main();
        main.solve();
        out.close();
    }
}