Problem:
Score : 300 points

Problem Statement

There are N cities on a 2D plane. The coordinate of the i-th city is (x_i, y_i). Here (x_1, x_2, \dots, x_N) and (y_1, y_2, \dots, y_N) are both permuations of (1, 2, \dots, N).

For each k = 1,2,\dots,N, find the answer to the following question:

Rng is in City k.
Rng can perform the following move arbitrarily many times:

move to another city that has a smaller x-coordinate and a smaller y-coordinate, or a larger x-coordinate and a larger y-coordinate, than the city he is currently in.

How many cities (including City k) are reachable from City k?

Constraints

1 \leq N \leq 200,000

(x_1, x_2, \dots, x_N) is a permutation of (1, 2, \dots, N).

(y_1, y_2, \dots, y_N) is a permutation of (1, 2, \dots, N).

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
:
x_N y_N

Output

Print N lines. In i-th line print the answer to the question when k = i.

Sample Input 1

4
1 4
2 3
3 1
4 2

Sample Output 1

1
1
2
2

Rng can reach City 4 from City 3, or conversely City 3 from City 4.

Sample Input 2

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

Sample Output 2

3
3
1
1
2
3
2

Solution in Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.nio.ByteBuffer;
import java.nio.charset.Charset;
import java.util.Map;
import java.util.NoSuchElementException;
import java.io.OutputStream;
import java.nio.CharBuffer;
import java.io.IOException;
import java.nio.charset.CharsetDecoder;
import java.lang.reflect.Field;
import java.nio.charset.StandardCharsets;
import java.io.UncheckedIOException;
import java.util.TreeMap;
import java.util.Map.Entry;
import java.security.AccessControlException;
import java.io.Writer;
import java.util.Comparator;
import java.io.InputStream;

/**
 * Built using CHelper reloaded plug-in
 * Actual solution is at the top
 *
 * @author mikit
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        LightScanner2 in = new LightScanner2(inputStream);
        LightWriter2 out = new LightWriter2(outputStream);
        AReachableTowns solver = new AReachableTowns();
        solver.solve(1, in, out);
        out.close();
    }

    static class AReachableTowns {
        public void solve(int testNumber, LightScanner2 in, LightWriter2 out) {
            int n = in.ints();
            AReachableTowns.City[] cities = new AReachableTowns.City[n];
            for (int i = 0; i < n; i++) {
                cities[i] = new AReachableTowns.City(i, in.ints(), in.ints());
            }
            IntUnionFind uf = new IntUnionFind(n);
            TreeMap<Integer, Integer> set = new TreeMap<>();
            IntroSort.sort(cities, Comparator.comparing(city -> city.x));
            for (int i = 0; i < n; i++) {
                Map.Entry<Integer, Integer> lo = set.lowerEntry(cities[i].y);
                if (lo != null) uf.union(cities[i].i, lo.getValue());
                set.put(cities[i].y, cities[i].i);
            }
            set.clear();
            for (int i = n - 1; i >= 0; i--) {
                Map.Entry<Integer, Integer> lo = set.higherEntry(cities[i].y);
                if (lo != null) uf.union(cities[i].i, lo.getValue());
                set.put(cities[i].y, cities[i].i);
            }

            for (int i = 0; i < n; i++) {
                out.ans(uf.size(i)).ln();
            }
        }

        private static class City {
            final int i;
            final int x;
            final int y;

            City(int i, int x, int y) {
                this.i = i;
                this.x = x;
                this.y = y;
            }

        }

    }

    static final class IntUnionFind {
        private int groups;
        private final int[] nodes;
        private final int[] rank;

        public IntUnionFind(int n) {
            groups = n;
            nodes = new int[n];
            Arrays.fill(nodes, -1);
            rank = new int[n];
        }

        public int find(int i) {
            int ans = nodes[i];
            if (ans < 0) {
                return i;
            } else {
                return nodes[i] = find(ans);
            }
        }

        public int size(int i) {
            return -nodes[find(i)];
        }

        public boolean union(int x, int y) {
            x = find(x);
            y = find(y);
            if (x == y) {
                return false;
            } else if (rank[x] < rank[y]) {
                nodes[y] += nodes[x];
                nodes[x] = y;
            } else if (rank[x] == rank[y]) {
                rank[x]++;
                nodes[x] += nodes[y];
                nodes[y] = x;
            } else {
                nodes[x] += nodes[y];
                nodes[y] = x;
            }
            groups--;
            return true;
        }

    }

    static interface Verified {
    }

    static abstract class LightScannerAdapter implements AutoCloseable {
        public abstract void close();

    }

    static class HeapSort {
        private HeapSort() {
        }

        private static <T> void heapfy(T[] a, int low, int high, int i, T val, Comparator<? super T> comparator) {
            int child = 2 * i - low + 1;
            while (child < high) {
                if (child + 1 < high && comparator.compare(a[child], a[child + 1]) < 0) {
                    child++;
                }
                if (comparator.compare(val, a[child]) >= 0) {
                    break;
                }
                a[i] = a[child];
                i = child;
                child = 2 * i - low + 1;
            }
            a[i] = val;
        }

        static <T> void sort(T[] a, int low, int high, Comparator<T> comparator) {
            for (int p = (high + low) / 2 - 1; p >= low; p--) {
                heapfy(a, low, high, p, a[p], comparator);
            }
            while (high > low) {
                high--;
                T pval = a[high];
                a[high] = a[low];
                heapfy(a, low, high, low, pval, comparator);
            }
        }

    }

    static class LightScanner2 extends LightScannerAdapter {
        private static final int BUF_SIZE = 1024 * 1024;
        private final InputStream stream;
        private final byte[] buf = new byte[BUF_SIZE];
        private int ptr;
        private int len;

        public LightScanner2(InputStream stream) {
            this.stream = stream;
        }

        private int read() {
            if (ptr < len) return buf[ptr++];
            try {
                ptr = 0;
                len = stream.read(buf);
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            if (len == -1) return -1;
            return buf[ptr++];
        }

        private void skip() {
            int b;
            while (isTokenSeparator(b = read()) && b != -1) ;
            if (b == -1) throw new NoSuchElementException("EOF");
            ptr--;
        }

        public int ints() {
            long x = longs();
            if (x < Integer.MIN_VALUE || Integer.MAX_VALUE < x) throw new NumberFormatException("Overflow");
            return (int) x;
        }

        public long longs() {
            skip();
            int b = read();
            boolean negate;
            if (b == '-') {
                negate = true;
                b = read();
            } else negate = false;
            long x = 0;
            for (; !isTokenSeparator(b); b = read()) {
                if ('0' <= b && b <= '9') x = x * 10 + b - '0';
                else throw new NumberFormatException("Unexpected character '" + b + "'");
            }
            return negate ? -x : x;
        }

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

        private static boolean isTokenSeparator(int b) {
            return b < 33 || 126 < b;
        }

    }

    static class LightWriter2 implements AutoCloseable {
        private static final int BUF_SIZE = 1024 * 1024;
        private static final int BUF_THRESHOLD = 64 * 1024;
        private final OutputStream out;
        private final byte[] buf = new byte[BUF_SIZE];
        private int ptr;
        private final Field fastStringAccess;
        private boolean autoflush = false;
        private boolean breaked = true;

        public LightWriter2(OutputStream out) {
            this.out = out;
            Field f;
            try {
                f = String.class.getDeclaredField("value");
                f.setAccessible(true);
                if (f.getType() != byte[].class) f = null;
            } catch (ReflectiveOperationException | AccessControlException ignored) {
                f = null;
            }
            this.fastStringAccess = f;
        }

        public LightWriter2(Writer out) {
            this.out = new LightWriter2.WriterOutputStream(out);
            this.fastStringAccess = null;
        }

        private void allocate(int n) {
            if (ptr + n <= BUF_SIZE) return;
            try {
                out.write(buf, 0, ptr);
                ptr = 0;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            if (BUF_SIZE < n) throw new IllegalArgumentException("Internal buffer exceeded");
        }

        public void close() {
            try {
                out.write(buf, 0, ptr);
                ptr = 0;
                out.flush();
                out.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

        public LightWriter2 print(char c) {
            allocate(1);
            buf[ptr++] = (byte) c;
            breaked = false;
            return this;
        }

        public LightWriter2 print(String s) {
            byte[] bytes;
            if (this.fastStringAccess == null) bytes = s.getBytes();
            else {
                try {
                    bytes = (byte[]) fastStringAccess.get(s);
                } catch (IllegalAccessException ignored) {
                    bytes = s.getBytes();
                }
            }
            int n = bytes.length;
            if (n <= BUF_THRESHOLD) {
                allocate(n);
                System.arraycopy(bytes, 0, buf, ptr, n);
                ptr += n;
                return this;
            }
            try {
                out.write(buf, 0, ptr);
                ptr = 0;
                out.write(bytes);
                out.flush();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        private int print(long l) {
            if (l == 0) {
                print('0');
                return 1;
            } else if (l < 0) {
                print('-');
                l = -l;
            }
            int n = 0;
            long t = l;
            while (t > 0) {
                t /= 10;
                n++;
            }
            allocate(n);
            for (int i = 1; i <= n; i++) {
                buf[ptr + n - i] = (byte) (l % 10 + '0');
                l /= 10;
            }
            ptr += n;
            return n;
        }

        public LightWriter2 ans(int i) {
            if (!breaked) {
                print(' ');
            }
            breaked = false;
            print(i);
            return this;
        }

        public LightWriter2 ln() {
            print(System.lineSeparator());
            breaked = true;
            if (autoflush) {
                try {
                    out.flush();
                } catch (IOException ex) {
                    throw new UncheckedIOException(ex);
                }
            }
            return this;
        }

        private static class WriterOutputStream extends OutputStream {
            final Writer writer;
            final CharsetDecoder decoder;

            WriterOutputStream(Writer writer) {
                this.writer = writer;
                this.decoder = StandardCharsets.UTF_8.newDecoder();
            }

            public void write(int b) throws IOException {
                writer.write(b);
            }

            public void write(byte[] b) throws IOException {
                writer.write(decoder.decode(ByteBuffer.wrap(b)).array());
            }

            public void write(byte[] b, int off, int len) throws IOException {
                writer.write(decoder.decode(ByteBuffer.wrap(b, off, len)).array());
            }

            public void flush() throws IOException {
                writer.flush();
            }

            public void close() throws IOException {
                writer.close();
            }

        }

    }

    static class QuickSort {
        private QuickSort() {
        }

        private static <T> void med(T[] a, int low, int x, int y, int z, Comparator<? super T> comparator) {
            if (comparator.compare(a[z], a[x]) < 0) {
                ArrayUtil.swap(a, low, x);
            } else if (comparator.compare(a[y], a[z]) < 0) {
                ArrayUtil.swap(a, low, y);
            } else {
                ArrayUtil.swap(a, low, z);
            }
        }

        static <T> int step(T[] a, int low, int high, Comparator<? super T> comparator) {
            int x = low + 1, y = low + (high - low) / 2, z = high - 1;
            if (comparator.compare(a[x], a[y]) < 0) {
                med(a, low, x, y, z, comparator);
            } else {
                med(a, low, y, x, z, comparator);
            }

            int lb = low + 1, ub = high;
            while (true) {
                while (comparator.compare(a[lb], a[low]) < 0) {
                    lb++;
                }
                ub--;
                while (comparator.compare(a[low], a[ub]) < 0) {
                    ub--;
                }
                if (lb >= ub) {
                    return lb;
                }
                ArrayUtil.swap(a, lb, ub);
                lb++;
            }
        }

    }

    static class InsertionSort {
        private InsertionSort() {
        }

        static <T> void sort(T[] a, int low, int high, Comparator<? super T> comparator) {
            for (int i = low; i < high; i++) {
                for (int j = i; j > low && comparator.compare(a[j - 1], a[j]) > 0; j--) {
                    ArrayUtil.swap(a, j - 1, j);
                }
            }
        }

    }

    static final class BitMath {
        private BitMath() {
        }

        public static int count(int v) {
            return Integer.bitCount(v);
        }

        public static int msb(int v) {
            if (v == 0) {
                throw new IllegalArgumentException("Bit not found");
            }
            v |= (v >> 1);
            v |= (v >> 2);
            v |= (v >> 4);
            v |= (v >> 8);
            v |= (v >> 16);
            return count(v) - 1;
        }

    }

    static final class ArrayUtil {
        private ArrayUtil() {
        }

        public static <T> void swap(T[] a, int x, int y) {
            T t = a[x];
            a[x] = a[y];
            a[y] = t;
        }

    }

    static class IntroSort {
        private static int INSERTIONSORT_THRESHOLD = 16;

        private IntroSort() {
        }

        static <T> void sort(T[] a, int low, int high, int maxDepth, Comparator<T> comparator) {
            while (high - low > INSERTIONSORT_THRESHOLD) {
                if (maxDepth-- == 0) {
                    HeapSort.sort(a, low, high, comparator);
                    return;
                }
                int cut = QuickSort.step(a, low, high, comparator);
                sort(a, cut, high, maxDepth, comparator);
                high = cut;
            }
            InsertionSort.sort(a, low, high, comparator);
        }

        public static <T> void sort(T[] a, Comparator<T> comparator) {
            if (a.length <= INSERTIONSORT_THRESHOLD) {
                InsertionSort.sort(a, 0, a.length, comparator);
            } else {
                sort(a, 0, a.length, 2 * BitMath.msb(a.length), comparator);
            }
        }

    }
}