Problem:
Score : 700 points

Problem Statement

Snuke is playing a puzzle game.
In this game, you are given a rectangular board of dimensions R × C, filled with numbers. Each integer i from 1 through N is written twice, at the coordinates (x_{i,1},y_{i,1}) and (x_{i,2},y_{i,2}).

The objective is to draw a curve connecting the pair of points where the same integer is written, for every integer from 1 through N.
Here, the curves may not go outside the board or cross each other.

Determine whether this is possible.

Constraints

1 ≤ R,C ≤ 10^8

1 ≤ N ≤ 10^5

0 ≤ x_{i,1},x_{i,2} ≤ R(1 ≤ i ≤ N)

0 ≤ y_{i,1},y_{i,2} ≤ C(1 ≤ i ≤ N)

All given points are distinct.

All input values are integers.

Input

Input is given from Standard Input in the following format:

R C N
x_{1,1} y_{1,1} x_{1,2} y_{1,2}
:
x_{N,1} y_{N,1} x_{N,2} y_{N,2}

Output

Print YES if the objective is achievable; print NO otherwise.

Sample Input 1

4 2 3
0 1 3 1
1 1 4 1
2 0 2 2

Sample Output 1

YES

The above figure shows a possible solution.

Sample Input 2

2 2 4
0 0 2 2
2 0 0 1
0 2 1 2
1 1 2 1

Sample Output 2

NO

Sample Input 3

5 5 7
0 0 2 4
2 3 4 5
3 5 5 2
5 5 5 4
0 3 5 1
2 2 4 4
0 5 4 1

Sample Output 3

YES

Sample Input 4

1 1 2
0 0 1 1
1 0 0 1

Sample Output 4

NO

Solution in Kotlin (1.0.0) (judge verdict: Wrong Answer)

import java.io.InputStream

val input = FastScanner()

fun main(args: Array<String>) = input.run {
    val rows = nextInt()
    val cols = nextInt()
    val n = nextInt()

    fun onBorder(r: Int, c: Int) = r !in (1 until rows) || c !in (1 until cols)

    fun toNumber(r: Int, c: Int) = when (r) {
        0 -> c
        rows -> rows + cols + (cols - c)
        else -> when (c) {
            0 -> 2 * rows + cols + (rows - r)
            else -> rows + r
        }
    }

    val a = mutableListOf<Pair<Int, Int>>()

    repeat(n) {
        val r1 = nextInt()
        val c1 = nextInt()
        val r2 = nextInt()
        val c2 = nextInt()
        if (onBorder(r1, c1) && onBorder(r2, c2)) {
            a += toNumber(r1, c1) to toNumber(r2, c2)
        }
    }

    val b = mutableListOf<Pair<Int, Int>>()

    a.forEachIndexed { index, pair ->
        b += pair.first to index
        b += pair.second to index
    }

    b.sortBy { it.first }

    val visited = IntArray(a.size) { -1 }

    var depth = 0

    b.forEach {
        if (visited[it.second] == -1) {
            visited[it.second] = depth
            depth++
        } else {
            depth--
            if (visited[it.second] != depth) {
                println("NO")
                return
            }
        }
    }

    println("YES")
}

class FastScanner(private val input: InputStream = System.`in`) {
    private val sb = StringBuilder()
    private val buffer = ByteArray(4096)
    private var pos = 0
    private var size = 0

    fun nextLong(): Long {
        var c = skipWhitespace()

        val sign = if (c == '-'.toInt()) {
            c = read()
            -1
        } else 1

        var ans = 0L

        while (c > ' '.toInt()) {
            ans = ans * 10 + c - '0'.toInt()
            c = read()
        }

        return sign * ans
    }

    fun nextInt() = nextLong().toInt()

    private fun skipWhitespace(): Int {
        while (true) {
            val c = read()
            if (c > ' '.toInt() || c < 0) return c
        }
    }

    private fun read(): Int {
        while (pos >= size) {
            if (size < 0) return -1
            size = input.read(buffer, 0, buffer.size)
            pos = 0
        }
        return buffer[pos++].toInt()
    }
}