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: Runtime Error)

@file:Suppress("NOTHING_TO_INLINE", "EXPERIMENTAL_FEATURE_WARNING", "OVERRIDE_BY_INLINE")

import java.io.PrintWriter
import kotlin.math.*
import kotlin.random.Random
import kotlin.collections.sort as _sort
import kotlin.collections.sortDescending as _sortDescending
import kotlin.io.println as iprintln

/** @author Spheniscine */
fun main() { _writer.solve(); _writer.flush() }
fun PrintWriter.solve() {
//    val numCases = readInt()
//    for(case in 1..numCases) {
//        //print("Case #$case: ")
//
//    }

    object {
        val nns = readInt()
        val nwe = readInt()

        val ns = Array(nns) { NS(readInt(), readInt(), readInt()) }
        val we = Array(nwe) { WE(readInt(), readInt(), readInt()) }



        val I = intListOf(-inf, 0)
        val J = intListOf(-inf, 0).also { J ->
            for ((i0, i1, j) in ns) {
                I.add(i0); I.add(i1); J.add(j)
            }

            for ((i, j0, j1) in we) {
                I.add(i); J.add(j0); J.add(j1)
            }
            I.sort()
            J.sort()
        }

        val n = I.size
        val m = J.size

        val rt = Array(n) { BooleanArray(m-1) { true } }
        val dn = Array(n-1) { BooleanArray(m) { true } }.also { dn ->
            for(seg in ns) {
                val i0 = I.lowerBound(seg.i0)
                val i1 = I.lowerBound(seg.i1)
                val j = J.lowerBound(seg.j)

                for(i in i0..i1) rt[i][j-1] = false
            }

            for(seg in we) {
                val i = I.lowerBound(seg.i)
                val j0 = J.lowerBound(seg.j0)
                val j1 = J.lowerBound(seg.j1)

                for(j in j0..j1) dn[i-1][j] = false
            }
        }

        inline fun forEachNeighbor(i: Int, j: Int, yield: (ni: Int, nj: Int) -> Unit) {
            if(i > 0 && dn[i-1][j]) yield(i-1, j)
            if(i < n-2 && dn[i][j]) yield(i+1, j)
            if(j > 0 && rt[i][j-1]) yield(i, j-1)
            if(j < m-2 && rt[i][j]) yield(i, j+1)
        }

        val G = Array(n-1) { BooleanArray(m-1) }.also { G ->
            val Q = IntDeque()
            val si = I.lowerBound(0)
            val sj = J.lowerBound(0)
            G[si][sj] = true
            Q.add(si); Q.add(sj)

            while (Q.isNotEmpty()) {
                val i = Q.remove()
                val j = Q.remove()

                forEachNeighbor(i, j) { ni, nj ->
                    if(!G[ni][nj]) {
                        G[ni][nj] = true
                        Q.add(ni); Q.add(nj)
                    }
                }
            }
        }

        val ans = run ans@{
            var ans = 0L
            for(i in 0 until n-1) {
                for(j in 0 until m-1) {
                    if(G[i][j]) {
                        if(i !in 1 until n-2 || j !in 1 until m-2) return@ans "INF"
                        ans += (I[i+1] - I[i]).toLong() * (J[j+1] - J[j])
                    }
                }
            }
            ans.toString()
        }.also { println(it) }

    }
}

data class NS(val i0: Int, val i1: Int, val j: Int)
data class WE(val i: Int, val j0: Int, val j1: Int)

const val inf = Int.MAX_VALUE

inline fun IntList.forEachRun(yield: (item: Int, num: Int) -> Unit) {
    if(isEmpty()) return
    var last = this[0]
    var num = 1

    for(i in 1 until size) {
        if(last == this[i]) num++
        else {
            yield(last, num)
            last = this[i]
            num = 1
        }
    }
    yield(last, num)
}

fun IntList.lowerBound(value: Int): Int {
    var bit = Integer.highestOneBit(size)
    var pos = 0

    while(bit > 0) {
        val npos = pos or bit
        if(npos <= size && this[npos-1] < value) pos = npos
        bit = bit shr 1
    }
    return pos
}

fun IntList.sortCompress() {
    sort()
    val t = IntList()
    forEachRun { item, _ ->
        t.add(item)
    }

    clear()
    for(item in t) add(item)
}

class IntList(initialCapacity: Int = 12) {
    private var _arr = IntArray(initialCapacity)
    private val capacity get() = _arr.size
    var size = 0
        private set
    inline val lastIndex get() = size - 1
    inline val indices get() = 0 until size

    constructor(copyFrom: IntArray): this(copyFrom.size) { copyFrom.copyInto(_arr); size = copyFrom.size }
    constructor(copyFrom: Collection<Int>): this(copyFrom.size) { _arr = copyFrom.toIntArray(); size = copyFrom.size }



    fun contentEquals(other: IntList): Boolean {
        return this === other || size == other.size && indices.all { this[it] == other[it] }
    }

    private fun grow(minCapacity: Int = 8) {
        val newCapacity = maxOf(minCapacity, capacity + (capacity shr 1))
        _arr = _arr.copyOf(newCapacity)
    }

    fun ensureCapacity(minCapacity: Int) { if(capacity < minCapacity) grow(minCapacity) }

    operator fun get(index: Int): Int {
        require(index in 0 until size)
        return _arr[index]
    }

    operator fun set(index: Int, value: Int) {
        require(index in 0 until size)
        _arr[index] = value
    }

    fun add(value: Int) {
        if(size == capacity) grow()
        _arr[size++] = value
    }

    fun add(index: Int, element: Int) {
        if(size == capacity) grow()
        _arr.copyInto(_arr, index + 1, index, size)
        size++
        set(index, element)
    }

    fun clear() { size = 0 }

    fun removeAt(index: Int): Int {
        val e = get(index)
        _arr.copyInto(_arr, index, index + 1, size)
        size--
        return e
    }

    operator fun iterator() = object: IntIterator() {
        private var pos = 0
        override fun hasNext() = pos < size
        override fun nextInt() = get(pos++)
    }

    inline fun isEmpty() = size == 0
    inline fun isNotEmpty() = size != 0

    fun pop() = _arr[--size]

    fun swap(i: Int, j: Int) { val t = this[i]; this[i] = this[j]; this[j] = t }
    fun reverse() {
        for(i in 0 until size / 2) swap(i, lastIndex - i)
    }

    fun shuffle(rnd: Random = random) = _shuffle(rnd, _arr::get, _arr::set, size)
    fun sort() { shuffle(); _arr._sort(0, size) }
    fun sortDescending() { sort(); reverse() }

    fun joinToString(separator: CharSequence) = if(size == 0) "" else let {
        buildString {
            append(it[0])
            for (i in 1 until size) {
                append(separator).append(it[i])
            }
        }
    }

    override fun toString() = "[" + joinToString(", ") + "]"

    fun toIntArray() = _arr.copyOf(size)
    fun toList() = List(size, ::get)

    inline fun first() = get(0)
    inline fun last() = get(lastIndex)
}

inline fun IntList(size: Int, init: (Int) -> Int) = IntList(size).apply {
    for(i in 0 until size) { add(init(i)) }
}
inline fun IntArray.toIntList() = IntList(this)
inline fun Collection<Int>.toIntList() = IntList(this)
inline fun intListOf(vararg values: Int) = IntList(values)

fun IntList.max() = (1 until size).fold(this[0]) { acc, i -> max(acc, this[i]) }
fun IntList.min() = (1 until size).fold(this[0]) { acc, i -> min(acc, this[i]) }
fun IntList.getOrNull(i: Int) = if(i in indices) get(i) else null
inline fun IntList.count(predicate: (Int) -> Boolean) = indices.count { predicate(this[it]) }
fun IntList.copyOf() = IntList(size, ::get)


class IntDeque(capacity: Int = 12){
    private var arr = IntArray(capacity)
    var size = 0
        private set
    inline val lastIndex get() = size - 1
    inline val indices get() = 0 until size

    private inline val capacity get() = arr.size

    inline fun isEmpty() = size == 0
    inline fun isNotEmpty() = size != 0

    private var head = 0

    private fun grow(minCapacity: Int = 8) {
        val newCapacity = maxOf(minCapacity, capacity + (capacity shr 1))
        val new = IntArray(newCapacity)
        for(i in 0 until size) new[i] = get(i)
        arr = new
        head = 0
    }

    private fun incHead() {
        head++
        if(head == capacity) head = 0
    }

    private fun decHead() {
        if(head == 0) head = capacity - 1
        else head--
    }

    private fun index(i: Int) = (head + i).let { if(it >= capacity) it - capacity else it }

    fun add(index: Int, element: Int) {
        if(size == capacity) grow()
        if(index < size / 2) {
            decHead()
            size++
            for(i in 0 until index) {
                set(i, get(i+1))
            }
        } else {
            size++
            for(i in size - 2 downTo index) {
                set(i+1, get(i))
            }
        }
        set(index, element)
    }

    fun addLast(e: Int) {
        if(size == capacity) grow()
        arr[index(size)] = e
        size++
    }
    inline fun add(e: Int) = addLast(e)

    val first get() = get(0)
    val last get() = get(lastIndex)

    fun removeFirst(): Int {
        val e = get(0)
        incHead()
        size--
        return e
    }
    inline fun remove() = removeFirst()
    fun removeLast(): Int {
        val e = get(lastIndex)
        size--
        return e
    }

    fun addFirst(e: Int) {
        if(size == capacity) grow()
        decHead()
        arr[head] = e
        size++
    }

    operator fun get(index: Int): Int {
        require(index in 0 until size)
        return arr[index(index)]
    }

    fun removeAt(index: Int): Int {
        val e = get(index)
        if(index < size / 2) {
            for(i in index - 1 downTo 0) {
                set(i+1, get(i))
            }
            incHead()
        } else {
            for(i in index until size - 1) {
                set(i, get(i+1))
            }
        }
        size--
        return e
    }

    operator fun set(index: Int, element: Int): Int {
        val old = get(index)
        arr[index(index)] = element
        return old
    }

    operator fun iterator() = object: IntIterator() {
        var i = 0
        override fun hasNext(): Boolean = i < size
        override fun nextInt(): Int = get(i++)
    }
}

/** IO */
//@JvmField val INPUT = File("input.txt").inputStream()
//@JvmField val OUTPUT = File("output.txt").outputStream()
@JvmField val INPUT = System.`in`
@JvmField val OUTPUT = System.out

const val _BUFFER_SIZE = 1 shl 16
@JvmField val _buffer = ByteArray(_BUFFER_SIZE)
@JvmField var _bufferPt = 0
@JvmField var _bytesRead = 0

tailrec fun readChar(): Char {
    if(_bufferPt == _bytesRead) {
        _bufferPt = 0
        _bytesRead = INPUT.read(_buffer, 0, _BUFFER_SIZE)
    }
    return if(_bytesRead < 0) Char.MIN_VALUE
    else {
        val c = _buffer[_bufferPt++].toChar()
        if (c == '\r') readChar()
        else c
    }
}

fun readLine(): String? {
    var c = readChar()
    return if(c == Char.MIN_VALUE) null
    else buildString {
        while(true) {
            when(c) {
                '\n', Char.MIN_VALUE -> return@buildString
                else -> {
                    append(c)
                    c = readChar()
                }
            }
        }
    }
}
fun readLn() = readLine()!!

fun read() = buildString {
    var c = readChar()
    while(c <= ' ') {
        if(c == Char.MIN_VALUE) return@buildString
        c = readChar()
    }
    do {
        append(c)
        c = readChar()
    } while(c > ' ')
}
fun readInt() = read().toInt()
fun readDouble() = read().toDouble()
fun readLong() = read().toLong()
fun readStrings(n: Int) = List(n) { read() }
fun readLines(n: Int) = List(n) { readLn() }
fun readInts(n: Int) = List(n) { read().toInt() }
fun readIntArray(n: Int) = IntArray(n) { read().toInt() }
fun readDoubles(n: Int) = List(n) { read().toDouble() }
fun readDoubleArray(n: Int) = DoubleArray(n) { read().toDouble() }
fun readLongs(n: Int) = List(n) { read().toLong() }
fun readLongArray(n: Int) = LongArray(n) { read().toLong() }

@JvmField val _writer = PrintWriter(OUTPUT, false)

/** shuffles and sort overrides to avoid quicksort attacks */
private inline fun <T> _shuffle(rnd: Random, get: (Int) -> T, set: (Int, T) -> Unit, size: Int) {
    // Fisher-Yates shuffle algorithm
    for (i in size - 1 downTo 1) {
        val j = rnd.nextInt(i + 1)
        val temp = get(i)
        set(i, get(j))
        set(j, temp)
    }
}

@JvmField var _random: Random? = null
val random get() = _random ?: Random(0x594E215C123 * System.nanoTime()).also { _random = it }

fun IntArray.shuffle(rnd: Random = random) = _shuffle(rnd, ::get, ::set, size)
fun IntArray.sort() { shuffle(); _sort() }
fun IntArray.sortDescending() { shuffle(); _sortDescending() }

fun LongArray.shuffle(rnd: Random = random) = _shuffle(rnd, ::get, ::set, size)
fun LongArray.sort() { shuffle(); _sort() }
fun LongArray.sortDescending() { shuffle(); _sortDescending() }

fun DoubleArray.shuffle(rnd: Random = random) = _shuffle(rnd, ::get, ::set, size)
fun DoubleArray.sort() { shuffle(); _sort() }
fun DoubleArray.sortDescending() { shuffle(); _sortDescending() }

fun CharArray.shuffle(rnd: Random = random) = _shuffle(rnd, ::get, ::set, size)
inline fun CharArray.sort() { _sort() }
inline fun CharArray.sortDescending() { _sortDescending() }

inline fun <T: Comparable<T>> Array<out T>.sort() = _sort()
inline fun <T: Comparable<T>> Array<out T>.sortDescending() = _sortDescending()
inline fun <T: Comparable<T>> MutableList<out T>.sort() = _sort()
inline fun <T: Comparable<T>> MutableList<out T>.sortDescending() = _sortDescending()

fun `please stop removing these imports IntelliJ`() { iprintln(max(1, 2)) }

/** additional commons */
inline fun <T> Iterable<T>.sumByLong(func: (T) -> Long) = fold(0L) { acc, t -> acc + func(t) }
inline fun <T> Sequence<T>.sumByLong(func: (T) -> Long) = fold(0L) { acc, t -> acc + func(t) }
inline fun <T> Array<T>.sumByLong(func: (T) -> Long) = fold(0L) { acc, t -> acc + func(t) }
fun IntArray.sumLong() = fold(0L, Long::plus)