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 Kotlin (1.3.71) (judge verdict: Time Limit Exceeded)

//package abc168.F

import java.io.*
import java.math.*
import java.util.*
import kotlin.math.*

var reader: BufferedReader = System.`in`.bufferedReader()
var writer: PrintWriter = PrintWriter(System.`out`)

fun next() = reader.readLine()!!
fun nextInt() = next().toInt()
fun nextLong() = next().toLong()
fun nextDouble() = next().toDouble()
fun nextStrings() = next().split(" ")
fun nextInts() = nextStrings().map { it.toInt() }
fun nextLongs() = nextStrings().map { it.toLong() }
fun nextDoubles() = nextStrings().map { it.toDouble() }

fun put(v: Any?) = writer.print(v)
fun puts() = writer.println()
fun puts(v: Any?) = writer.println(v)

var debug = false
fun dp(v: Any?) {
    if (debug) println(v)
}
fun dp() {
    if (debug) println()
}

tailrec fun gcd(a: Long, b: Long): Long {
    if(b == 0L) return a
    return gcd(b, a % b)
}

class ModInt(
    val value: Long
) {
    private val POW = mutableMapOf<Int, ModInt>()

    constructor (value: Int): this(value.toLong())

    operator fun plus(rhs: ModInt): ModInt {
        return ModInt((value + rhs.value) % M)
    }
    operator fun minus(rhs: ModInt): ModInt {
        return ModInt((value - rhs.value + M) % M)
    }
    operator fun times(rhs: ModInt): ModInt {
        return ModInt((value * rhs.value) % M)
    }
    operator fun div(rhs: ModInt): ModInt {
        return ModInt(value * inv(rhs.value) % M)
    }
    private fun inv(v: Long): Long {
        return INV.computeIfAbsent(v) {
            M - (((M / v) * inv(M % v)) % M)
        }
    }
    fun pow(v: Int): ModInt {
        return POW.computeIfAbsent(v) {
            var result = 1L
            var x = v
            var vv = value
            while (x != 0) {
                if ((x and 1) != 0) {
                    result = (result * vv) % M
                }
                vv = (vv * vv) % M
                x = x ushr 1
            }
            ModInt(result)
        }
    }

    override fun toString(): String {
        return value.toString()
    }

    companion object {
        private const val M = 1000000007L

        private val INV = mutableMapOf<Long, Long>().also {
            it[1] = 1
        }

        val ZERO = ModInt(0)
        val ONE = ModInt(1)
    }
}

fun test(case: Int, input: String, expected: String) {
    reader = input.trimIndent().reader().buffered()

    val stringWriter = StringWriter()
    writer = PrintWriter(stringWriter)

    solve()
    writer.flush()

    val actual = stringWriter.toString()

    println("[test $case]")
    if ("${expected}" == actual) {
        println("OK")
    } else {
        println("NG")
        println()
        println("expected: \"${expected}\"")
        println("actual:   \"${actual}\"")
    }
    println()
}

fun main(args: Array<String>) {
    if ((args.size == 1) && (args[0] == "test")) {
        testAll()
    } else {
        solve()
        writer.flush()
    }
}

///////////////////////////////////////////////////////////

fun testAll() {
    debug = true

    test(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
    """,
    "13")
    test(2,
    """
    6 1
    -3 -1 -2
    -3 -1 1
    -2 -1 2
    1 4 -2
    1 4 -1
    1 4 1
    3 1 4
    """,
    "INF")
}

fun <T> readToList(n: Int, transformer: (List<Long>) -> T): MutableList<T> {
    return mutableListOf<T>().also { list ->
        repeat(n) {
            val lines = nextLongs()
            list.add(transformer(lines))
        }
    }
}

class Indexer(
    val X: Int,
    val Y: Int
) {
    operator fun invoke(x: Int, y: Int): Int {
        return y * X + x
    }

    fun <T> contentToString(arr: Array<T>): String {
        val builder = StringBuilder()

        builder.appendln("----------")
        for (y in 0 until Y) {
            for (x in 0 until X) {
                builder.append(arr[this(x, y)])
                builder.append(", ")
            }
            builder.appendln()
        }
        builder.append("----------")

        return builder.toString()
    }
}

val TOP = 1
val BOTTOM = 2
val LEFT = 4
val RIGHT = 8

typealias Line = Pair<Long, Long>
typealias Point = Pair<Int, Int>

fun covered(l: Long, r: Long, lines: List<Line>): Boolean {
    for (line in lines) {
        if (l < line.first) {
            break
        }
        if (r <= line.second) {
            return true
        }
    }
    return false
}

fun doSolve(): Long {

    val (N, M) = nextInts()

    val horizontal = TreeMap<Long, MutableList<Line>>().let { map ->
        repeat(N) {
            val (a, b, c) = nextLongs()

            map.compute(c) { _, list ->
                (list ?: mutableListOf<Line>()).also {
                    it.add(Line(a, b))
                }
            }
        }
        map.entries.map { (c, lines) ->
            c to lines.sortedBy(Line::first)
        }
    }

    val vertical = TreeMap<Long, MutableList<Line>>().let { map ->
        repeat(M) {
            val (d, e, f) = nextLongs()

            map.compute(d) { _, list ->
                (list ?: mutableListOf<Line>()).also {
                    it.add(Line(e, f))
                }
            }
        }
        map.entries.map { (d, lines) ->
            d to lines.sortedBy(Line::first)
        }
    }

    dp(horizontal)
    dp(vertical)

    val X = vertical.size + 2
    val Y = horizontal.size + 2
    val index = Indexer(X, Y)

    val areas =  Array<Long>(X*Y) { -1 }
    val walls =  Array<Int>(X*Y) { 0 }

    var startX = 0
    var startY = 0

    for (tmpY in 0 until horizontal.size-1) {
        val y = tmpY + 1
        val (c1, hLines1) = horizontal[tmpY]
        val (c2, hLines2) = horizontal[tmpY+1]

        for (tmpX in 0 until vertical.size-1) {
            val x = tmpX + 1
            //dp("-- $x, $y")
            val (d1, vLines1) = vertical[tmpX]
            val (d2, vLines2) = vertical[tmpX+1]

            val area = (c2 - c1) * (d2 - d1)
            areas[index(x, y)] = area

            var wall = 0
            if (covered(d1, d2, hLines2)) {
                wall = (wall or TOP)
            }
            if (covered(d1, d2, hLines1)) {
                wall = (wall or BOTTOM)
            }
            if (covered(c1, c2, vLines1)) {
                wall = (wall or LEFT)
            }
            if (covered(c1, c2, vLines2)) {
                wall = (wall or RIGHT)
            }
            walls[index(x, y)] = wall

            if ((c1 <= 0) && (0 < c2) && (d1 <= 0) && (0 < d2)) {
                startX = x
                startY = y
            }
        }
    }

    //dp("[$X, $Y]")
    //dp("${index.contentToString(areas)}")
    //dp("${index.contentToString(walls)}")
    //dp("$startX, $startY")
    dp()

    var area = 0L
    val visited = mutableSetOf<Point>()

    val queue = ArrayDeque<Pair<Int, Int>>()
    queue.add(Pair(startX, startY))

    while (!queue.isEmpty()) {
        val p= queue.remove()
        dp("pop: $p")
        if (!visited.add(p)) {
            continue;
        }

        val (x, y) = p
        val a = areas[index(x, y)]
        dp("area: $a")
        if (a < 0) {
            return -1
        }

        area += a
        dp("-> $area")

        val wall = walls[index(x, y)]
        dp("wall: $wall")
        if ((wall and TOP) == 0) {
            dp("queue: ($x, ${y+1})")
            queue.add(Point(x, y+1))
        }
        if ((wall and BOTTOM) == 0) {
            dp("queue: ($x, ${y-1})")
            queue.add(Point(x, y-1))
        }
        if ((wall and LEFT) == 0) {
            dp("queue: (${x-1}, $y)")
            queue.add(Point(x-1, y))
        }
        if ((wall and RIGHT) == 0) {
            dp("queue: (${x+1}, $y)")
            queue.add(Point(x+1, y))
        }

        dp()
    }

    return area
}

fun solve() {
    val ret = doSolve()
    if (ret >= 0) {
        put(ret)
    } else {
        put("INF")
    }
}