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 C# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.InteropServices;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;

public static class P
{
    public static void Main()
    {
        var nm = Console.ReadLine().Split().Select(int.Parse).ToArray();
        var n = nm[0];
        var m = nm[1];
        List<long> xAxis = new List<long>() { int.MinValue, 0, int.MaxValue };
        List<long> yAxis = new List<long>() { int.MinValue, 0, int.MaxValue };

        (long y1, long y2, long x)[] tate = new (long y1, long y2, long x)[n];
        for (int i = 0; i < n; i++)
        {
            var abc = Console.ReadLine().Split().Select(int.Parse).ToArray();
            tate[i] = (abc[0], abc[1], abc[2]);
            yAxis.Add(tate[i].y1);
            yAxis.Add(tate[i].y2);
            xAxis.Add(tate[i].x);
        }

        (long y, long x1, long x2)[] yoko = new (long y, long x1, long x2)[m];
        for (int i = 0; i < m; i++)
        {
            var def = Console.ReadLine().Split().Select(int.Parse).ToArray();
            yoko[i] = (def[0], def[1], def[2]);
            yAxis.Add(yoko[i].y);
            xAxis.Add(yoko[i].x1);
            xAxis.Add(yoko[i].x2);
        }

        xAxis = xAxis.Distinct().OrderBy(x => x).ToList();
        yAxis = yAxis.Distinct().OrderBy(x => x).ToList();

        var yTotal = yAxis.Count - 1;
        var xTotal = xAxis.Count - 1;

        HashSet<Tuple<int, int>> removedEdge = new HashSet<Tuple<int, int>>();

        int Encode(int y, int x) => y * xTotal + x;

        foreach (var (y1, y2, x) in tate)
        {
            var xInd = xAxis.BinarySearch(x);
            var yStart = yAxis.BinarySearch(y1);
            var yEnd = yAxis.BinarySearch(y2);
            for (int y = yStart; y < yEnd; y++)
            {
                var a = Encode(y, xInd - 1);
                var b = Encode(y, xInd);
                removedEdge.Add(new Tuple<int, int>(a, b));
            }
        }

        foreach (var (y, x1, x2) in yoko)
        {
            var yInd = yAxis.BinarySearch(y);
            var xStart = xAxis.BinarySearch(x1);
            var xEnd = xAxis.BinarySearch(x2);
            for (int x = xStart; x < xEnd; x++)
            {
                var a = Encode(yInd - 1, x);
                var b = Encode(yInd, x);
                removedEdge.Add(new Tuple<int, int>(a, b));
            }
        }

        UnionFind uf = new UnionFind(yTotal * xTotal);
        for (int i = 0; i < yTotal - 1; i++)
            for (int j = 0; j < xTotal; j++)
            {
                var id = i * xTotal + j; 
                if (removedEdge.Contains(new Tuple<int, int>(id, id + xTotal))) continue; 
                uf.TryUnite(id, id + xTotal);
                //Console.WriteLine($"{id} {id + xTotal}");
            }
        for (int i = 0; i < yTotal; i++)
            for (int j = 0; j < xTotal - 1; j++)
            {
                var id = i * xTotal + j;
                if (removedEdge.Contains(new Tuple<int, int>(id, id + 1))) continue; 
                uf.TryUnite(id, id + 1); 
                //Console.WriteLine($"{id} {id + 1}");
            }


        var ushiID = uf.Find(Encode(yAxis.BinarySearch(0), xAxis.BinarySearch(0)));
        if (ushiID == uf.Find(0))
        {
            Console.WriteLine("INF");
            return;
        }
        long res = 0;
        for (int i = 0; i < uf.Size; i++)
        {
            if (ushiID != uf.Find(i)) continue;
            var yInd = i / xTotal;
            var xInd = i % xTotal;
            res += (xAxis[xInd + 1] - xAxis[xInd]) * (yAxis[yInd + 1] - yAxis[yInd]);
        }
        Console.WriteLine(res);
    }
}


class UnionFind
{
    public int Size { get; private set; }
    public int GroupCount { get; private set; }
    public IEnumerable<int> AllRepresents => Parent.Where((x, y) => x == y);
    int[] Sizes;
    int[] Parent;
    public UnionFind(int count)
    {
        Size = count;
        GroupCount = count;
        Parent = new int[count];
        Sizes = new int[count];
        for (int i = 0; i < count; i++) Sizes[Parent[i] = i] = 1;
    }
    public bool TryUnite(int x, int y)
    {
        int xp = Find(x);
        int yp = Find(y);
        if (yp == xp) return false;
        if (Sizes[xp] < Sizes[yp]) { var tmp = xp; xp = yp; yp = tmp; }
        GroupCount--;
        Parent[yp] = xp;
        Sizes[xp] += Sizes[yp];
        return true;
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public int GetSize(int x) => Sizes[Find(x)];
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public int Find(int x)
    {
        while (x != Parent[x]) x = (Parent[x] = Parent[Parent[x]]);
        return x;
    }
}


struct Vector
{
    public long x;
    public long y;
    public long this[int index]
    {
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        get { if (index == 0) return x; else return y; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        set { if (index == 0) x = value; else y = value; }
    }
    public long Length => x * x + y * y;
    public double SqrtLength => Math.Sqrt(Length);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public Vector(long x, long y) { this.x = x; this.y = y; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public Vector RotateVector(double radian) => new Vector((long)(x * Math.Cos(radian) - y * Math.Sin(radian)), (long)(x * Math.Sin(radian) + y * Math.Cos(radian)));
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    static public long CrossProduct(Vector a, Vector b) => a.x * b.y - a.y * b.x;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    static public long InnerProduct(Vector a, Vector b) => a.x * b.x + a.y * b.y;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static Vector operator +(Vector a, Vector b) => new Vector(a.x + b.x, a.y + b.y);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static Vector operator -(Vector a, Vector b) => new Vector(a.x - b.x, a.y - b.y);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool operator ==(Vector a, Vector b) => a.x == b.x && a.y == b.y;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool operator !=(Vector a, Vector b) => a.x != b.x || a.y != b.y;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public override bool Equals(object obj) => this == (Vector)obj;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public override int GetHashCode() => x.GetHashCode() * 1000000007 + y.GetHashCode();
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public override string ToString() => $"({x},{y})";
}