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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.Collection;
import java.io.IOException;
import java.util.Deque;
import java.util.ArrayList;
import java.io.UncheckedIOException;
import java.util.List;
import java.util.TreeMap;
import java.io.Closeable;
import java.util.Map;
import java.io.Writer;
import java.util.Map.Entry;
import java.io.OutputStreamWriter;
import java.util.ArrayDeque;
import java.io.InputStream;

/**
 * Built using CHelper plug-in Actual solution is at the top
 * 
 * @author daltao
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "daltao", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            TaskC solver = new TaskC();
            solver.solve(1, in, out);
            out.close();
        }
    }
    static class TaskC {
        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            int a = in.readInt() - 1;
            int b = in.readInt() - 1;

            long[][] pts = new long[n][2];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < 2; j++) {
                    pts[i][j] = in.readInt();
                }
                long x = pts[i][0] + pts[i][1];
                long y = pts[i][0] - pts[i][1];
                pts[i][0] = x;
                pts[i][1] = y;
            }

            TreeMap<Long, TreeMap<Long, long[]>> x2y = new TreeMap<>();
            TreeMap<Long, TreeMap<Long, long[]>> y2x = new TreeMap<>();

            List<long[]> visited = new ArrayList<>(n);
            Deque<long[]> pending = new ArrayDeque<>(n);
            pending.addLast(pts[a]);
            pending.addLast(pts[b]);
            for (int i = 0; i < n; i++) {
                if (i == a || i == b) {
                    continue;
                }
                putInto(pts[i][0], pts[i][1], pts[i], x2y);
                putInto(pts[i][1], pts[i][0], pts[i], y2x);
            }

            long dist = chebyshev(pts[a], pts[b]);
            while (!pending.isEmpty()) {
                long[] pt = pending.removeFirst();
                visited.add(pt);

                // consider l side
                remove(x2y, y2x, pt[0] - dist, pt[1] - dist, pt[1] + dist, pending);
                remove(x2y, y2x, pt[0] + dist, pt[1] - dist, pt[1] + dist, pending);
                remove(y2x, x2y, pt[1] - dist, pt[0] - dist, pt[0] + dist, pending);
                remove(y2x, x2y, pt[1] + dist, pt[0] - dist, pt[0] + dist, pending);
            }

            TreeMap<Long, TreeMap<Long, Integer>> y2xRank = new TreeMap<>();
            TreeMap<Long, TreeMap<Long, Integer>> x2yRank = new TreeMap<>();
            visited.sort((a1, a2) -> Long.compare(a1[0], a2[0]));
            for (long[] pt : visited) {
                TreeMap<Long, Integer> inner = y2xRank.get(pt[1]);
                if (inner == null) {
                    inner = new TreeMap<>();
                    y2xRank.put(pt[1], inner);
                }
                inner.put(pt[0], inner.size() + 1);
            }
            visited.sort((a1, a2) -> Long.compare(a1[1], a2[1]));
            for (long[] pt : visited) {
                TreeMap<Long, Integer> inner = x2yRank.get(pt[0]);
                if (inner == null) {
                    inner = new TreeMap<>();
                    x2yRank.put(pt[0], inner);
                }
                inner.put(pt[1], inner.size() + 1);
            }

            long ans = 0;
            for (long[] pt : visited) {
                long local = countOf(x2yRank, pt[0] - dist, pt[1] - dist, pt[1] + dist)
                                + countOf(x2yRank, pt[0] + dist, pt[1] - dist, pt[1] + dist)
                                + countOf(y2xRank, pt[1] - dist, pt[0] - dist + 1, pt[0] + dist - 1)
                                + countOf(y2xRank, pt[1] + dist, pt[0] - dist + 1, pt[0] + dist - 1);
                ans += local;
            }

            out.println(ans / 2);
        }

        public int countOf(TreeMap<Long, TreeMap<Long, Integer>> map, Long k, Long l, Long r) {
            if (l > r) {
                return 0;
            }
            TreeMap<Long, Integer> inner = map.get(k);
            if (inner == null) {
                return 0;
            }
            Map.Entry<Long, Integer> floor = inner.ceilingEntry(l);
            Map.Entry<Long, Integer> ceil = inner.floorEntry(r);
            if (floor == null || ceil == null) {
                return 0;
            }
            return Math.max(0, ceil.getValue() - floor.getValue() + 1);
        }

        public void remove(TreeMap<Long, TreeMap<Long, long[]>> map, TreeMap<Long, TreeMap<Long, long[]>> opp, Long k1,
                        Long l, Long r, Deque<long[]> pending) {
            TreeMap<Long, long[]> inner = map.get(k1);
            if (inner == null) {
                return;
            }
            while (true) {
                Long y = inner.ceilingKey(l);
                if (y == null || y > r) {
                    break;
                }
                pending.addLast(inner.remove(y));
                opp.get(y).remove(k1);
            }
        }

        public void putInto(Long k1, Long k2, long[] pt, TreeMap<Long, TreeMap<Long, long[]>> map) {
            TreeMap<Long, long[]> inner = map.get(k1);
            if (inner == null) {
                inner = new TreeMap<>();
                map.put(k1, inner);
            }
            inner.put(k2, pt);
        }

        public long chebyshev(long[] a, long[] b) {
            return Math.max(Math.abs(a[0] - b[0]), Math.abs(a[1] - b[1]));
        }

    }
    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }
    static class FastOutput implements AutoCloseable, Closeable {
        private StringBuilder cache = new StringBuilder(1 << 20);
        private final Writer os;

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput println(long c) {
            cache.append(c).append('\n');
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

    }
}