Problem: 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.

Examples

Input

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


Output

4


Input

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


Output

4


Input

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


Output

7

Solution (in JAVA):

Solution:

import java.io.*;
import java.math.*;
import java.util.*;
import java.util.Map.Entry;

import static java.util.Arrays.*;

public class Main {
	private static final int mod = (int)1e9+7;

	final Random random = new Random(0);
	final IOFast io = new IOFast();

	/// MAIN CODE
	public void run() throws IOException {
//		int TEST_CASE = Integer.parseInt(new String(io.nextLine()).trim());
		int TEST_CASE = 1;
		while(TEST_CASE-- != 0) {
			int n = io.nextInt();
			int a = io.nextInt() - 1;
			int b = io.nextInt() - 1;
			x = new int[n];
			y = new int[n];
			TreeSet<Integer> sx = new TreeSet<>();
			TreeSet<Integer> sy = new TreeSet<>();
			for (int i = 0; i < n; i++) {
				x[i] = io.nextInt();
				y[i] = io.nextInt();
				
				// 45
				int yy = x[i];
				int xx = y[i];
				x[i] = xx - yy;
				y[i] = xx + yy;

				sx.add(x[i]);
				sy.add(y[i]);
			}
			
			for (int xx : sx) {
				xy.put(xx, new TreeMap<Integer, Integer>());
				xys.put(xx, new ArrayList<Integer>());
			}
			
			for (int yy : sy) {
				yx.put(yy, new TreeMap<Integer, Integer>());
				yxs.put(yy, new ArrayList<Integer>());
			}
			
			for (int i = 0; i < n; i++) {
				xy.get(x[i]).put(y[i], i);
				yx.get(y[i]).put(x[i], i);
				xys.get(x[i]).add(y[i]);
				yxs.get(y[i]).add(x[i]);
			}

			for (List<Integer> l : xys.values()) Collections.sort(l);
			for (List<Integer> l : yxs.values()) Collections.sort(l);
			
			// max(|dx|, |dy|)
			d = Math.max(Math.abs(x[a]-x[b]), Math.abs(y[a]-y[b]));
			io.out.println(dfs(a) / 2);
		}
	}

	int d;
	int[] x, y;
	TreeSet<Integer> vis = new TreeSet<>();
	TreeMap<Integer, TreeMap<Integer, Integer>> xy = new TreeMap<>();
	TreeMap<Integer, TreeMap<Integer, Integer>> yx = new TreeMap<>();
	TreeMap<Integer, List<Integer>> xys = new TreeMap<>();
	TreeMap<Integer, List<Integer>> yxs = new TreeMap<>();
	
	long dfs(int p) {
		if (!vis.add(p)) return 0;
		
		long ans = 0;

		{
			for (int s = -1; s <= 1; s += 2) {
				TreeMap<Integer, Integer> t = xy.get(x[p]+s*d);
				if (t == null) continue;
				
				List<Integer> li = xys.get(x[p]+s*d);
				int l = Collections.binarySearch(li, y[p]-d);
				int r = Collections.binarySearch(li, y[p]+d+1);
				if (l < 0) l = -l - 1;
				if (r < 0) r = -r - 1;
//				dump(x[p], y[p], d, li.get(l), li.get(r-1));
				ans += r - l;
				
				for (int cur = y[p]-d; cur <= y[p]+d; cur++) {
					Entry<Integer, Integer> e = t.ceilingEntry(cur);
					if (e == null || e.getKey() > y[p]+d) break;
					t.remove(e.getKey());
					cur = e.getKey();
//					dump(p, idx);
					ans += dfs(e.getValue());
				}
			}
			for (int s = -1; s <= 1; s += 2) {
				TreeMap<Integer, Integer> t = yx.get(y[p]+s*d);
				if (t == null) continue;
				
				List<Integer> li = yxs.get(y[p]+s*d);
				int l = Collections.binarySearch(li, x[p]-d+1);
				int r = Collections.binarySearch(li, x[p]+d);
				if (l < 0) l = -l - 1;
				if (r < 0) r = -r - 1;
				ans += r - l;
				
				for (int cur = x[p]-d; cur <= x[p]+d; cur++) {
					Entry<Integer, Integer> e = t.ceilingEntry(cur);
					if (e == null || e.getKey() > x[p]+d) break;
					t.remove(e.getKey());
					cur = e.getKey();
//					dump(p, idx);
					ans += dfs(e.getValue());
				}
			}
		}
		
//		for (int j = 0; j < 1; j++) {
//			final int pq = p;
//			
//			for (int cur = x[pq]-d-1; cur <= x[pq]+d-1; ) {
//				Entry<Integer, TreeMap<Integer, Integer>> e = xy.higherEntry(cur);
//				if (e == null || e.getKey() > x[pq]+d) break;
//				cur = e.getKey();
//				
//				{
//					TreeMap<Integer, Integer> s = e.getValue();
//					Integer idx = s.get(y[pq]-d);
//					if (idx != null) {
////						dump(p, idx);
//						add(pq, idx);
//						ans += 1 + dfs(idx);
//					}
//				}
//				
//				{
//					TreeMap<Integer, Integer> s = e.getValue();
//					Integer idx = s.get(y[pq]+d);
//					if (idx != null) {
////						dump(p, idx);
//						add(pq, idx);
//						ans += 1 + dfs(idx);
//					}
//				}
//			}
//			
//			for (int cur = y[pq]-d-1; cur <= y[pq]+d-1; ) {
//				Entry<Integer, TreeMap<Integer, Integer>> e = yx.higherEntry(cur);
//				if (e == null || e.getKey() > y[pq]+d) break;
//				cur = e.getKey();
//				
//				{
//					TreeMap<Integer, Integer> s = e.getValue();
//					Integer idx = s.get(x[pq]-d);
//					if (idx != null) {
////						dump(p, idx);
//						add(pq, idx);
//						ans += 1 + dfs(idx);
//					}
//				}
//				
//				{
//					TreeMap<Integer, Integer> s = e.getValue();
//					Integer idx = s.get(x[pq]+d);
//					if (idx != null) {
////						dump(p, idx);
//						add(pq, idx);
//						ans += 1 + dfs(idx);
//					}
//				}
//			}
//		}
		
		return ans;
	}
	

	/// TEMPLATE
	static int gcd(int n, int r) { return r == 0 ? n : gcd(r, n%r); }
	static long gcd(long n, long r) { return r == 0 ? n : gcd(r, n%r); }
	
	static <T> void swap(T[] x, int i, int j) { T t = x[i]; x[i] = x[j]; x[j] = t; }
	static void swap(int[] x, int i, int j) { int t = x[i]; x[i] = x[j]; x[j] = t; }

	void printArrayLn(int[] xs) { for(int i = 0; i < xs.length; i++) io.out.print(xs[i] + (i==xs.length-1?"\n":" ")); }
	void printArrayLn(long[] xs) { for(int i = 0; i < xs.length; i++) io.out.print(xs[i] + (i==xs.length-1?"\n":" ")); }
	
	static void dump(Object... o) { System.err.println(Arrays.deepToString(o)); } 
	
	void main() throws IOException {
		//		IOFast.setFileIO("rle-size.in", "rle-size.out");
		try { run(); }
		catch (EndOfFileRuntimeException e) { }
		io.out.flush();
	}
	public static void main(String[] args) throws IOException { new Main().main(); }
	
	static class EndOfFileRuntimeException extends RuntimeException {
		private static final long serialVersionUID = -8565341110209207657L; }

	static
	public class IOFast {
		private BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		private PrintWriter out = new PrintWriter(System.out);

		void setFileIn(String ins) throws IOException { in.close(); in = new BufferedReader(new FileReader(ins)); }
		void setFileOut(String outs) throws IOException { out.flush(); out.close(); out = new PrintWriter(new FileWriter(outs)); }
		void setFileIO(String ins, String outs) throws IOException { setFileIn(ins); setFileOut(outs); }

		private static int pos, readLen;
		private static final char[] buffer = new char[1024 * 8];
		private static char[] str = new char[500*8*2];
		private static boolean[] isDigit = new boolean[256];
		private static boolean[] isSpace = new boolean[256];
		private static boolean[] isLineSep = new boolean[256];

		static { for(int i = 0; i < 10; i++) { isDigit['0' + i] = true; } isDigit['-'] = true; isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true; isLineSep['\r'] = isLineSep['\n'] = true; }
		public int read() throws IOException { if(pos >= readLen) { pos = 0; readLen = in.read(buffer); if(readLen <= 0) { throw new EndOfFileRuntimeException(); } } return buffer[pos++]; }
		public int nextInt() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); int i = 0; int ret = 0; if(str[0] == '-') { i = 1; } for(; i < len; i++) ret = ret * 10 + str[i] - '0'; if(str[0] == '-') { ret = -ret; } return ret; }
		public long nextLong() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); int i = 0; long ret = 0; if(str[0] == '-') { i = 1; } for(; i < len; i++) ret = ret * 10 + str[i] - '0'; if(str[0] == '-') { ret = -ret; } return ret; }
		public char nextChar() throws IOException { while(true) { final int c = read(); if(!isSpace[c]) { return (char)c; } } }
		int reads(int len, boolean[] accept) throws IOException { try { while(true) { final int c = read(); if(accept[c]) { break; } if(str.length == len) { char[] rep = new char[str.length * 3 / 2]; System.arraycopy(str, 0, rep, 0, str.length); str = rep; } str[len++] = (char)c; } } catch(EndOfFileRuntimeException e) { ; } return len; }
		int reads(char[] cs, int len, boolean[] accept) throws IOException { try { while(true) { final int c = read(); if(accept[c]) { break; } cs[len++] = (char)c; } } catch(EndOfFileRuntimeException e) { ; } return len; }
		public char[] nextLine() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isLineSep); try { if(str[len-1] == '\r') { len--; read(); } } catch(EndOfFileRuntimeException e) { ; } return Arrays.copyOf(str, len); }
		public String nextString() throws IOException { return new String(next()); }
		public char[] next() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); return Arrays.copyOf(str, len); }
//		public int next(char[] cs) throws IOException { int len = 0; cs[len++] = nextChar(); len = reads(cs, len, isSpace); return len; }
		public double nextDouble() throws IOException { return Double.parseDouble(nextString()); }
		public long[] nextLongArray(final int n) throws IOException { final long[] res = new long[n]; for(int i = 0; i < n; i++) { res[i] = nextLong(); } return res; }
		public int[] nextIntArray(final int n) throws IOException { final int[] res = new int[n]; for(int i = 0; i < n; i++) { res[i] = nextInt(); } return res; }
		public int[][] nextIntArray2D(final int n, final int k) throws IOException { final int[][] res = new int[n][]; for(int i = 0; i < n; i++) { res[i] = nextIntArray(k); } return res; }
		public int[][] nextIntArray2DWithIndex(final int n, final int k) throws IOException { final int[][] res = new int[n][k+1]; for(int i = 0; i < n; i++) { for(int j = 0; j < k; j++) { res[i][j] = nextInt(); } res[i][k] = i; } return res; }
		public double[] nextDoubleArray(final int n) throws IOException { final double[] res = new double[n]; for(int i = 0; i < n; i++) { res[i] = nextDouble(); } return res; }
	}
}