Problem:
Score: 600 points

Problem Statement

There is a grass field that stretches infinitely.

In this field, there is a negligibly small cow. Let (x, y) denote the point that is x\ \mathrm{cm} south and y\ \mathrm{cm} east of the point where the cow stands now. The cow itself is standing at (0, 0).

There are also N north-south lines and M east-west lines drawn on the field. The i-th north-south line is the segment connecting the points (A_i, C_i) and (B_i, C_i), and the j-th east-west line is the segment connecting the points (D_j, E_j) and (D_j, F_j).

What is the area of the region the cow can reach when it can move around as long as it does not cross the segments (including the endpoints)? If this area is infinite, print INF instead.

Constraints

All values in input are integers between -10^9 and 10^9 (inclusive).

1 \leq N, M \leq 1000

A_i < B_i\ (1 \leq i \leq N)

E_j < F_j\ (1 \leq j \leq M)

The point (0, 0) does not lie on any of the given segments.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1 C_1
:
A_N B_N C_N
D_1 E_1 F_1
:
D_M E_M F_M

Output

If the area of the region the cow can reach is infinite, print INF; otherwise, print an integer representing the area in \mathrm{cm^2}.

(Under the constraints, it can be proved that the area of the region is always an integer if it is not infinite.)

Sample Input 1

5 6
1 2 0
0 1 1
0 2 2
-3 4 -1
-2 6 3
1 0 1
0 1 2
2 0 2
-1 -4 5
3 -2 4
1 2 4

Sample Output 1

13

The area of the region the cow can reach is 13\ \mathrm{cm^2}.

Sample Input 2

6 1
-3 -1 -2
-3 -1 1
-2 -1 2
1 4 -2
1 4 -1
1 4 1
3 1 4

Sample Output 2

INF

The area of the region the cow can reach is infinite.

Solution in Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.*;
import java.util.*;

class Solver {
  final int n, m;
  final int[][] abcs, defs;

  Solver(int n, int m, int[][] abcs, int[][] defs) {
    this.n = n;
    this.m = m;
    this.abcs = abcs;
    this.defs = defs;
  }

  private static final int[] DX = new int[]{1, 0, -1, 0};
  private static final int[] DY = new int[]{0, 1, 0, -1};

  public String solve() {
    Set<Integer> xSet = new HashSet<>();
    Set<Integer> ySet = new HashSet<>();
    xSet.add(-2_000_000_000);
    xSet.add(2_000_000_000);
    ySet.add(-2_000_000_000);
    ySet.add(2_000_000_000);
    for (int[] abc : abcs) {
      int a = abc[0];
      int b = abc[1];
      int c = abc[2];
      xSet.add(a);
      xSet.add(b);
      ySet.add(c);
    }
    for (int[] def : defs) {
      int d = def[0];
      int e = def[1];
      int f = def[2];
      xSet.add(d);
      ySet.add(e);
      ySet.add(f);
    }
    int xSize = xSet.size();
    int ySize = ySet.size();
    List<Integer> xList = new ArrayList<>();
    List<Integer> yList = new ArrayList<>();
    xList.addAll(xSet);
    yList.addAll(ySet);
    xSet = null;
    ySet = null;
    Collections.sort(xList);
    Collections.sort(yList);
    Map<Integer, Integer> xMap = new HashMap<>();
    Map<Integer, Integer> yMap = new HashMap<>();
    for (int i = 0; i < xSize; i++) {
      xMap.put(xList.get(i), i);
    }
    for (int i = 0; i < ySize; i++) {
      yMap.put(yList.get(i), i);
    }

    boolean[][] blocker = new boolean[2 * xSize][2 * ySize];
    for (int i = 0; i < xSize; i++) {
      for (int j = 0; j < ySize; j++) {
        blocker[2 * i][2 * j] = true;
      }
    }
    for (int[] def : defs) {
      int d = def[0];
      int e = def[1];
      int f = def[2];
      int xIndex = xMap.get(d);
      int yIndexMin = yMap.get(e);
      int yIndexMax = yMap.get(f);
      for (int y = yIndexMin; y < yIndexMax; y++) {
        blocker[2 * xIndex][2 * y + 1] = true;
      }
    }
    for (int[] abc : abcs) {
      int a = abc[0];
      int b = abc[1];
      int c = abc[2];
      int yIndex = yMap.get(c);
      int xIndexMin = xMap.get(a);
      int xIndexMax = xMap.get(b);
      for (int x = xIndexMin; x < xIndexMax; x++) {
        blocker[2 * x + 1][2 * yIndex] = true;
      }
    }
    xMap = null;
    yMap = null;

    int startXIndex = -1;
    for (int i = 1; i < xSize; i++) {
      if (xList.get(i - 1) < 0 && 0 <= xList.get(i)) {
        startXIndex = 2 * (i - 1) + 1;
        break;
      }
    }

    int startYIndex = -1;
    for (int i = 1; i < ySize; i++) {
      if (yList.get(i - 1) < 0 && 0 <= yList.get(i)) {
        startYIndex = 2 * (i - 1) + 1;
        break;
      }
    }

    long answer = 0;
    Deque<Integer> xIndexStack = new ArrayDeque<>();
    Deque<Integer> yIndexStack = new ArrayDeque<>();
    boolean[][] enqueued = new boolean[2 * xSize][2 * ySize];
    enqueued[startXIndex][startYIndex] = true;
    xIndexStack.add(startXIndex);
    yIndexStack.add(startYIndex);
    while (!xIndexStack.isEmpty()) {
      int xIndex = xIndexStack.pollLast();
      int yIndex = yIndexStack.pollLast();
      if (xIndex == 0 || yIndex == 0 || xIndex == 2 * xSize - 1 || yIndex == 2 * ySize - 1) {
        return "INF";
      }
      if (xIndex % 2 == 1 && yIndex % 2 == 1) {
        long xMax = xList.get(xIndex / 2 + 1);
        long xMin = xList.get(xIndex / 2);
        long yMax = yList.get(yIndex / 2 + 1);
        long yMin = yList.get(yIndex / 2);
        answer += (xMax - xMin) * (yMax - yMin);  
      }
      for (int k = 0; k < 4; k++) {
        int nextXIndex = xIndex + DX[k];
        int nextYIndex = yIndex + DY[k];
        if (!blocker[nextXIndex][nextYIndex] && !enqueued[nextXIndex][nextYIndex]) {
          enqueued[nextXIndex][nextYIndex] = true;
          xIndexStack.add(nextXIndex);
          yIndexStack.add(nextYIndex);
        }
      }
    }
    return Long.toString(answer);
  }
}

public class Main {
  private static void execute(ContestReader reader, ContestWriter out) {
    int n = reader.nextInt();
    int m = reader.nextInt();
    int[][] abcs = reader.nextInt(n, 3);
    int[][] defs = reader.nextInt(m, 3);
    out.println(new Solver(n, m, abcs, defs).solve());
  }
  
  public static void main(String[] args) {
    ContestReader reader = new ContestReader(System.in);
    ContestWriter out = new ContestWriter(System.out);
    execute(reader, out);
    out.flush();
  }
}

class ContestWriter extends PrintWriter {
  ContestWriter(PrintStream printeStream) {
    super(printeStream);
  }

  public void printList(List<? extends Object> list) {
    for (Object object : list) {
      println(object);
    }
  }

  public void printListOneLine(List<? extends Object> list) {
    List<String> stringList = new ArrayList<>();
    for (Object object : list) {
      stringList.add(object.toString());
    }
    println(String.join(" ", stringList));
  }
}

class ContestReader {
  private static final int BUFFER_SIZE = 1024;
  
  private final InputStream stream;
  private final byte[] buffer;
  private int pointer;
  private int bufferLength;
  
  ContestReader(InputStream stream) {
    this.stream = stream;
    this.buffer = new byte[BUFFER_SIZE];
    this.pointer = 0;
    this.bufferLength = 0;
  }
  
  private boolean hasNextByte() {
    if (pointer < bufferLength) {
      return true;
    }
    
    pointer = 0;
    try {
      bufferLength = stream.read(buffer);
    } catch (IOException e) {
      throw new RuntimeException(e);
    }
    return bufferLength > 0;
  }
  
  private int readByte() {
    if (hasNextByte()) {
      return buffer[pointer++];
    } else {
      return -1;
    }
  }
  
  private static boolean isPrintableChar(int c) {
    return 33 <= c && c <= 126;
  }
  
  public boolean hasNext() {
    while (hasNextByte() && !isPrintableChar(buffer[pointer])) {
      pointer++;
    }
    return hasNextByte();
  }
  
  public String next() {
    if (!hasNext()) {
      throw new NoSuchElementException();
    }
    StringBuilder sb = new StringBuilder();
    while(true) {
      int b = readByte();
      if (!isPrintableChar(b)) {
        break;
      }
      sb.appendCodePoint(b);
    }
    return sb.toString();
  }
  
  public String nextLine() {
    if (!hasNext()) {
      throw new NoSuchElementException();
    }
    StringBuilder sb = new StringBuilder();
    while(true) {
      int b = readByte();
      if (!isPrintableChar(b) && b != 0x20) {
        break;
      }
      sb.appendCodePoint(b);
    }
    return sb.toString();
  }
  
  public char nextChar() {
    return next().charAt(0);
  }
  
  public int nextInt() {
    if (!hasNext()) {
      throw new NoSuchElementException();
    }
    
    int n = 0;
    boolean minus = false;
    
    {
      int b = readByte();
      if (b == '-') {
        minus = true;
      } else if ('0' <= b && b <= '9') {
        n = b - '0';
      } else {
        throw new NumberFormatException();
      }
    }
    
    while(true){
      int b = readByte();
      if ('0' <= b && b <= '9') {
        n *= 10;
        n += b - '0';
      } else if (b == -1 || !isPrintableChar(b)) {
        return minus ? -n : n;
      } else {
        throw new NumberFormatException();
      }
    }
  }
  
  public long nextLong() {
    if (!hasNext()) {
      throw new NoSuchElementException();
    }
    
    long n = 0;
    boolean minus = false;
    
    {
      int b = readByte();
      if (b == '-') {
        minus = true;
      } else if ('0' <= b && b <= '9') {
        n = b - '0';
      } else {
        throw new NumberFormatException();
      }
    }
    
    while(true){
      int b = readByte();
      if ('0' <= b && b <= '9') {
        n *= 10;
        n += b - '0';
      } else if (b == -1 || !isPrintableChar(b)) {
        return minus ? -n : n;
      } else {
        throw new NumberFormatException();
      }
    }
  }
  
  public double nextDouble() {
    return Double.parseDouble(next());
  }
  
  public String[] next(int n) {
    String[] array = new String[n];
    for (int i = 0; i < n; i++) {
      array[i] = next();
    }
    return array;
  }
  
  public String[] nextLine(int n) {
    String[] array = new String[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextLine();
    }
    return array;
  }
  
  public char[] nextChar(int n) {
    char[] array = new char[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextChar();
    }
    return array;
  }
  
  public int[] nextInt(int n) {
    int[] array = new int[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextInt();
    }
    return array;
  }
  
  public long[] nextLong(int n) {
    long[] array = new long[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextLong();
    }
    return array;
  }
  
  public double[] nextDouble(int n) {
    double[] array = new double[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextDouble();
    }
    return array;
  }
  
  public char[] nextCharArray() {
    return next().toCharArray();
  }
  
  public String[][] next(int n, int m) {
    String[][] matrix = new String[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = next();
      }
    }
    return matrix;
  }
  
  public int[][] nextInt(int n, int m) {
    int[][] matrix = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextInt();
      }
    }
    return matrix;
  }
  
  public char[][] nextChar(int n, int m) {
    char[][] matrix = new char[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextChar();
      }
    }
    return matrix;
  }
  
  public long[][] nextLong(int n, int m) {
    long[][] matrix = new long[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextLong();
      }
    }
    return matrix;
  }
  
  public double[][] nextDouble(int n, int m) {
    double[][] matrix = new double[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextDouble();
      }
    }
    return matrix;
  }
  
  public char[][] nextCharArray(int n) {
    char[][] matrix = new char[n][];
    for (int i = 0; i < n; i++) {
      matrix[i] = next().toCharArray();
    }
    return matrix;
  }
}