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.util.*;

public class Main {

	static int dist(int[] p1, int[] p2) {
		return Math.max(Math.abs(p1[0] - p2[0]), Math.abs(p1[1] - p2[1]));
	}

	static int[][] pts;
	static int D;
	static TreeMap<Integer, TreeSet<int[]>> adjXMap, adjYMap;
	static TreeMap<Integer, ArrayList<Integer>> adjXL, adjYL;

	static boolean[] visited;

	static void dfs(int u) {
		if (visited[u])
			return;
		visited[u] = true;

		int x = pts[u][0], y = pts[u][1];
		for (int t = x - D; t <= x + D; t += 2 * D) {
			TreeSet<int[]> adjX = adjXMap.get(t);

			if (adjX == null)
				continue;
			while (true) {
				int[] v = adjX.ceiling(new int[] { 0, y - D });
				if (v == null || v[1] > y + D)
					break;

				adjX.remove(v);
//				int y2 = v[1];
//				TreeSet<int[]> adjY = adjYMap.get(y2);
//
//				adjY.remove(new int[] { v[0], t });
				dfs(v[0]);

			}

		}
		for (int t = y - D; t <= y + D; t += 2 * D) {
			TreeSet<int[]> adjY = adjYMap.get(t);
			if (adjY == null)
				continue;
			while (true) {
				int[] v = adjY.ceiling(new int[] { 0, x - D });
				if (v == null || v[1] > x + D)
					break;

				adjY.remove(v);
//				int x2 = v[1];
//				TreeSet<int[]> adjX = adjXMap.get(x2);
//
//				adjX.remove(new int[] { v[0], t });
				dfs(v[0]);

			}

		}
	}

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner();
		PrintWriter out = new PrintWriter(System.out);
		int n = sc.nextInt(), a = sc.nextInt() - 1, b = sc.nextInt() - 1;
		pts = new int[n][2];
		for (int i = 0; i < n; i++) {
			int x = sc.nextInt(), y = sc.nextInt();
			pts[i][0] = x + y;
			pts[i][1] = y - x;
		}
		D = dist(pts[a], pts[b]);

		adjXMap = new TreeMap();
		adjYMap = new TreeMap<Integer, TreeSet<int[]>>();
		adjXL = new TreeMap();
		adjYL = new TreeMap();

		for (int i = 0; i < n; i++) {

			int x = pts[i][0], y = pts[i][1];

			if (adjXMap.containsKey(x)) {
				adjXMap.get(x).add(new int[] { i, y });
			} else {
				TreeSet<int[]> set = new TreeSet<>((f, s) -> f[1] != s[1] ? f[1] - s[1] : f[0] - s[0]);
				set.add(new int[] { i, y });
				adjXMap.put(x, set);
			
			}

		}
		for (int i = 0; i < n; i++) {
			int x = pts[i][0], y = pts[i][1];

			if (adjYMap.containsKey(y)) {
				adjYMap.get(y).add(new int[] { i, x });
			} else {
				TreeSet<int[]> set = new TreeSet<>((f, s) -> f[1] != s[1] ? f[1] - s[1] : f[0] - s[0]);
				set.add(new int[] { i, x });
				adjYMap.put(y, set);
				
			}

		}
		visited = new boolean[n];
		dfs(a);
		adjXMap.clear();
		adjYMap.clear();
		for (int i = 0; i < n; i++) {

			int x = pts[i][0], y = pts[i][1];

			if (adjXL.containsKey(x)) {
				adjXL.get(x).add(y);
			} else {

				ArrayList<Integer> l = new ArrayList();
				l.add(y);
				adjXL.put(x, l);
			}

		}
		for (int i = 0; i < n; i++) {
			int x = pts[i][0], y = pts[i][1];

			if (adjYL.containsKey(y)) {
				adjYL.get(y).add(x);
			} else {

				ArrayList<Integer> l = new ArrayList();
				l.add(x);
				adjYL.put(y, l);
			}

		}
		long edges = 0;
		for (ArrayList<Integer> l : adjXL.values())
			Collections.sort(l);
		for (ArrayList<Integer> l : adjYL.values())
			Collections.sort(l);
		for (int i = 0; i < n; i++)
			if (visited[i]) {
				int lo, hi;
				int x = pts[i][0], y = pts[i][1];
				for (int t : new int[] { x - D, x + D }) {
					int yMin = y - D + 1, yMax = y + D - 1;
					ArrayList<Integer> adj = adjXL.get(t);
					if (adj == null)
						continue;
					int first = 0, last = -1;
					lo = 0;
					hi = adj.size() - 1;
					while (lo <= hi) {
						int mid = lo + hi >> 1;
						if (adj.get(mid) < yMin)
							lo = mid + 1;
						else if (adj.get(mid) > yMax)
							hi = mid - 1;
						else {
							first = mid;
							hi = mid - 1;
						}
					}
					lo = 0;
					hi = adj.size() - 1;
					while (lo <= hi) {
						int mid = lo + hi >> 1;
						if (adj.get(mid) < yMin)
							lo = mid + 1;
						else if (adj.get(mid) > yMax)
							hi = mid - 1;
						else {
							last = mid;
							lo = mid + 1;
						}

					}
					edges += last - first + 1;
				}
				for (int t : new int[] { y - D, y + D }) {
					int xMin = x - D, xMax = x + D;
					ArrayList<Integer> adj = adjYL.get(t);
					if (adj == null)
						continue;
					int first = 0, last = -1;
					lo = 0;
					hi = adj.size() - 1;
					while (lo <= hi) {
						int mid = lo + hi >> 1;
						if (adj.get(mid) < xMin)
							lo = mid + 1;
						else if (adj.get(mid) > xMax)
							hi = mid - 1;
						else {
							first = mid;
							hi = mid - 1;
						}
					}
					lo = 0;
					hi = adj.size() - 1;
					while (lo <= hi) {
						int mid = lo + hi >> 1;
						if (adj.get(mid) < xMin)
							lo = mid + 1;
						else if (adj.get(mid) > xMax)
							hi = mid - 1;
						else {
							last = mid;
							lo = mid + 1;
						}

					}
					edges += last - first + 1;
				}
			}
		System.out.println(edges >> 1);
		out.close();

	}

	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		Scanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		Scanner(String fileName) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(fileName));
		}

		String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		String nextLine() throws IOException {
			return br.readLine();
		}

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

		long nextLong() throws NumberFormatException, IOException {
			return Long.parseLong(next());
		}

		double nextDouble() throws NumberFormatException, IOException {
			return Double.parseDouble(next());
		}

		boolean ready() throws IOException {
			return br.ready();
		}

		int[] nxtArr(int n) throws IOException {
			int[] ans = new int[n];
			for (int i = 0; i < n; i++)
				ans[i] = nextInt();
			return ans;
		}

	}

	static void sort(int[] a) {
		shuffle(a);
		Arrays.sort(a);
	}

	static void shuffle(int[] a) {
		int n = a.length;
		Random rand = new Random();
		for (int i = 0; i < n; i++) {
			int tmpIdx = rand.nextInt(n);
			int tmp = a[i];
			a[i] = a[tmpIdx];
			a[tmpIdx] = tmp;
		}
	}

}