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: Time Limit Exceeded)

import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.Closeable;
import java.io.FileInputStream;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map.Entry;
import java.util.Queue;
import java.util.TreeMap;

public class Main implements Runnable{
	static ContestScanner in;static Writer out;
	public static void main(String[] args) {
		new Thread(null, new Main(), "", 16 * 1024 * 1024).start();
	}
	public void run() {
		try {
			in = new ContestScanner();
			out = new Writer();
			Main solve = new Main();
			solve.solve();
			in.close();
			out.flush();
			out.close();
		} catch (IOException e) {
			e.printStackTrace();
		}
	}
	static void dump(int[]a){StringBuilder s=new StringBuilder();for(int i=0;i<a.length;i++)
	s.append(a[i]).append(" ");out.println(s.toString().trim());}
	static void dump(int[]a,int n){for(int i=0;i<a.length;i++)out.printf("%"+n+"d ",a[i]);out.println();}
	static void dump(long[]a){StringBuilder s=new StringBuilder();for(int i=0;i<a.length;i++)
	s.append(a[i]).append(" ");out.println(s.toString().trim());}
	static void dump(char[]a){for(int i=0;i<a.length;i++)out.print(a[i]);out.println();}
	static long pow(long a,int n){long r=1;while(n>0){if((n&1)==1)r*=a;a*=a;n>>=1;}return r;}
	static String itob(int a,int l){return String.format("%"+l+"s",Integer.toBinaryString(a)).replace(' ','0');}
	static void sort(int[]a){m_sort(a,0,a.length,new int[a.length]);}
	static void sort(int[]a,int l){m_sort(a,0,l,new int[l]);}
	static void sort(int[]a,int l,int[]buf){m_sort(a,0,l,buf);}
	static void sort(int[]a,int s,int l,int[]buf){m_sort(a,s,l,buf);}
	static void m_sort(int[]a,int s,int sz,int[]b)
	{if(sz<7){for(int i=s;i<s+sz;i++)for(int j=i;j>s&&a[j-1]>a[j];j--)swap(a, j, j-1);return;}
	m_sort(a,s,sz/2,b);m_sort(a,s+sz/2,sz-sz/2,b);int idx=s;int l=s,r=s+sz/2;final int le=s+sz/2,re=s+sz;
	while(l<le&&r<re){if(a[l]>a[r])b[idx++]=a[r++];else b[idx++]=a[l++];}
	while(r<re)b[idx++]=a[r++];while(l<le)b[idx++]=a[l++];for(int i=s;i<s+sz;i++)a[i]=b[i];
	} /* qsort(3.5s)<<msort(9.5s)<<<shuffle+qsort(17s)<Arrays.sort(Integer)(20s) */
	static void sort(long[]a){m_sort(a,0,a.length,new long[a.length]);}
	static void sort(long[]a,int l){m_sort(a,0,l,new long[l]);}
	static void sort(long[]a,int l,long[]buf){m_sort(a,0,l,buf);}
	static void sort(long[]a,int s,int l,long[]buf){m_sort(a,s,l,buf);}
	static void m_sort(long[]a,int s,int sz,long[]b)
	{if(sz<7){for(int i=s;i<s+sz;i++)for(int j=i;j>s&&a[j-1]>a[j];j--)swap(a, j, j-1);return;}
	m_sort(a,s,sz/2,b);m_sort(a,s+sz/2,sz-sz/2,b);int idx=s;int l=s,r=s+sz/2;final int le=s+sz/2,re=s+sz;
	while(l<le&&r<re){if(a[l]>a[r])b[idx++]=a[r++];else b[idx++]=a[l++];}
	while(r<re)b[idx++]=a[r++];while(l<le)b[idx++]=a[l++];for(int i=s;i<s+sz;i++)a[i]=b[i];}
	static void swap(long[] a,int i,int j){final long t=a[i];a[i]=a[j];a[j]=t;}
	static void swap(int[] a,int i,int j){final int t=a[i];a[i]=a[j];a[j]=t;}
	static int binarySearchSmallerMax(int[]a,int v)// get maximum index which a[idx]<=v
	{int l=-1,r=a.length-1,s=0;while(l<=r){int m=(l+r)/2;if(a[m]>v)r=m-1;else{l=m+1;s=m;}}return s;}
	static int binarySearchSmallerMax(int[]a,int v,int l,int r)
	{int s=-1;while(l<=r){int m=(l+r)/2;if(a[m]>v)r=m-1;else{l=m+1;s=m;}}return s;}
	@SuppressWarnings("unchecked")
	static List<Integer>[]createGraph(int n)
    {List<Integer>[]g=new List[n];for(int i=0;i<n;i++)g[i]=new ArrayList<>();return g;}
	void solve() throws IOException{
		int n = in.nextInt();
		int a = in.nextInt()-1;
		int b = in.nextInt()-1;
		x = new long[n];
		y = new long[n];
		for(int i=0; i<n; i++){
			Pos p = new Pos(in.nextDouble(), in.nextDouble());
			p.rotate(Math.PI/4);
			p.scale(Math.sqrt(2));
			x[i] = (long)(Math.round(p.x));
			y[i] = (long)(Math.round(p.y));
			put(x[i], y[i], i);
		}
		createNewMap();
		dist = Math.max(Math.abs(x[a]-x[b]), Math.abs(y[a]-y[b]));
		boolean[] used = new boolean[n];
		used[a] = true;
		used[b] = true;
		Queue<Integer> qu = new ArrayDeque<>(n);
		stack = new int[n*2];
		HashSet<Integer>[] edge = new HashSet[n];
		for(int i=0; i<n; i++){
			edge[i] = new HashSet<>();
		}
		edge[a].add(b);
		edge[b].add(a);
		qu.add(a);
		qu.add(b);
		while(!qu.isEmpty()){
			final int id = qu.poll();
			setNexts(id);
			while(sp>0){
				final int next = stack[--sp];
				edge[id].add(next);
				edge[next].add(id);
				if(used[next]) continue;
				used[next] = true;
				qu.add(next);
			}
		}
		long ans = 0;
		for(int i=0; i<n; i++){
			ans += edge[i].size();
		}
		System.out.println(ans/2);
	}
	
	long[] x, y;
	long dist;
	int[] stack;
	int sp;
	void setNexts(int from){
		sp = 0;
		setAxis(y[from]-dist, y[from]+dist, xMap.get(x[from]-dist));
		setAxis(y[from]-dist, y[from]+dist, xMap.get(x[from]+dist));
		setAxis(x[from]-dist, x[from]+dist, yMap.get(y[from]-dist));
		setAxis(x[from]-dist, x[from]+dist, yMap.get(y[from]+dist));
	}
	
	final int mask = (1<<20)-1;
	void setAxis(long from, long to, long[] ord){
		if(ord==null) return;
		int begin = Arrays.binarySearch(ord, from<<20);
		if(begin<0){
			begin = -begin-1;
		}
		final long brd = to+1<<20;
		for(int i=begin; i<ord.length && ord[i]<brd; i++){
			stack[sp++] = (int)(ord[i] & mask);
		}
	}
	
	TreeMap<Long, TreeMap<Long, Integer>> mapX = new TreeMap<>();
	TreeMap<Long, TreeMap<Long, Integer>> mapY = new TreeMap<>();
	void put(long x, long y, int id){
		TreeMap<Long, Integer> mx, my;
		if(mapX.containsKey(x)){
			mx = mapX.get(x);
		}else{
			mx = new TreeMap<>();
			mapX.put(x, mx);
		}
		if(mapY.containsKey(y)){
			my = mapY.get(y);
		}else{
			my = new TreeMap<>();
			mapY.put(y, my);
		}
		mx.put(y, id);
		my.put(x, id);
	}
	
	HashMap<Long, long[]> xMap, yMap;
	void createNewMap(){
		xMap = createNewMap(mapX);
		yMap = createNewMap(mapY);
	}
	
	HashMap<Long, long[]> createNewMap(TreeMap<Long, TreeMap<Long, Integer>> map){
		HashMap<Long, long[]> res = new HashMap<>(map.size());
		for(Entry<Long, TreeMap<Long, Integer>> e: map.entrySet()){
			res.put(e.getKey(), toArray(e.getValue()));
		}
		return res;
	}
	
	long[] toArray(TreeMap<Long, Integer> map){
		long[] res = new long[map.size()];
		int p = 0;
		for(Entry<Long, Integer> e: map.entrySet()){
			res[p++] = e.getKey()<<20 | e.getValue();
		}
		return res;
	}
}

class Pos implements Comparable<Pos>{
	static final double EPS = 1e-10;
	double x, y;
	public Pos(double x, double y){
		this.x = x;
		this.y = y;
	}
	public double dist2(Pos p){
		return (x-p.x)*(x-p.x) + (y-p.y)*(y-p.y);
	}
	public void scale(double s){
		x *= s;
		y *= s;
	}
	public void rotate(double rad){
		final double newX = x*Math.cos(rad) - y*Math.sin(rad);
		final double newY = x*Math.sin(rad) + y*Math.cos(rad);
		x = newX;
		y = newY;
	}
	public void move(double dx, double dy){
		x += dx;
		y += dy;
	}
	@Override
	public int compareTo(Pos o) {
		if(Math.abs(x-o.x) >= EPS) return Double.compare(x, o.x);
		if(Math.abs(y-o.y) >= EPS) return Double.compare(y, o.y);
		return 0;
	}
	@Override
	public String toString() {
		return String.format("(%5f, %5f)", x, y);
	}
}

@SuppressWarnings("serial")
class MultiSet<T> extends HashMap<T, Integer>{
	@Override public Integer get(Object key){return containsKey(key)?super.get(key):0;}
	public void add(T key,int v){put(key,get(key)+v);}
	public void add(T key){put(key,get(key)+1);}
	public void sub(T key){final int v=get(key);if(v==1)remove(key);else put(key,v-1);}
	public MultiSet<T> merge(MultiSet<T> set)
	{MultiSet<T>s,l;if(this.size()<set.size()){s=this;l=set;}else{s=set;l=this;}
	for(Entry<T,Integer>e:s.entrySet())l.add(e.getKey(),e.getValue());return l;}
}
@SuppressWarnings("serial")
class OrderedMultiSet<T> extends TreeMap<T, Integer>{
	@Override public Integer get(Object key){return containsKey(key)?super.get(key):0;}
	public void add(T key,int v){put(key,get(key)+v);}
	public void add(T key){put(key,get(key)+1);}
	public void sub(T key){final int v=get(key);if(v==1)remove(key);else put(key,v-1);}
	public OrderedMultiSet<T> merge(OrderedMultiSet<T> set)
	{OrderedMultiSet<T>s,l;if(this.size()<set.size()){s=this;l=set;}else{s=set;l=this;}
	while(!s.isEmpty()){l.add(s.firstEntry().getKey(),s.pollFirstEntry().getValue());}return l;}
}
class Pair implements Comparable<Pair>{
	int a,b;final int hash;Pair(int a,int b){this.a=a;this.b=b;hash=(a<<16|a>>16)^b;}
	public boolean equals(Object obj){Pair o=(Pair)(obj);return a==o.a&&b==o.b;}
	public int hashCode(){return hash;}
	public int compareTo(Pair o){if(a!=o.a)return a<o.a?-1:1;else if(b!=o.b)return b<o.b?-1:1;return 0;}
}
class Timer{
	long time;public void set(){time=System.currentTimeMillis();}
	public long stop(){return time=System.currentTimeMillis()-time;}
	public void print(){System.out.println("Time: "+(System.currentTimeMillis()-time)+"ms");}
	@Override public String toString(){return"Time: "+time+"ms";}
}
class Writer extends PrintWriter{
	public Writer(String filename)throws IOException
	{super(new BufferedWriter(new FileWriter(filename)));}
	public Writer()throws IOException{super(System.out);}
}
class ContestScanner implements Closeable{
	private BufferedReader in;private int c=-2;
	public ContestScanner()throws IOException 
	{in=new BufferedReader(new InputStreamReader(System.in));}
	public ContestScanner(String filename)throws IOException
	{in=new BufferedReader(new InputStreamReader(new FileInputStream(filename)));}
	public String nextToken()throws IOException {
		StringBuilder sb=new StringBuilder();
		while((c=in.read())!=-1&&Character.isWhitespace(c));
		while(c!=-1&&!Character.isWhitespace(c)){sb.append((char)c);c=in.read();}
		return sb.toString();
	}
	public String readLine()throws IOException{
		StringBuilder sb=new StringBuilder();if(c==-2)c=in.read();
		while(c!=-1&&c!='\n'&&c!='\r'){sb.append((char)c);c=in.read();}
		return sb.toString();
	}
	public long nextLong()throws IOException,NumberFormatException
	{return Long.parseLong(nextToken());}
	public int nextInt()throws NumberFormatException,IOException
	{return(int)nextLong();}
	public double nextDouble()throws NumberFormatException,IOException 
	{return Double.parseDouble(nextToken());}
	public void close() throws IOException {in.close();}
}