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 Go (1.6) (judge verdict: Accepted)

package main

import (
	. "fmt"
	"io"
	"os"
	"sort"
)

type event struct{ p, i, d int }
type events []event

func (p events) Len() int           { return len(p) }
func (p events) Less(i, j int) bool { return p[i].p < p[j].p }
func (p events) Swap(i, j int)      { p[i], p[j] = p[j], p[i] }

// github.com/EndlessCheng/codeforces-go
func run(_r io.Reader, _w io.Writer) {
	buf := make([]byte, 16384)
	_i := len(buf)
	rc := func() byte {
		if _i == len(buf) {
			_r.Read(buf)
			_i = 0
		}
		b := buf[_i]
		_i++
		return b
	}
	ri := func() (x int) {
		b := rc()
		for ; '0' > b || b > '9'; b = rc() {
		}
		for ; '0' <= b && b <= '9'; b = rc() {
			x = x*10 + int(b&15)
		}
		return
	}
	r, c, n := ri(), ri(), ri()
	border := func(x, y int) bool { return x == 0 || x == r || y == 0 || y == c }
	getP := func(x, y int) int {
		if y == 0 || x == r {
			return x + y
		}
		return 2*r + 2*c - x - y
	}
	es := events{}
	for i := 0; i < n; i++ {
		x1, y1, x2, y2 := ri(), ri(), ri(), ri()
		if border(x1, y1) && border(x2, y2) {
			p1, p2 := getP(x1, y1), getP(x2, y2)
			if p1 > p2 {
				p1, p2 = p2, p1
			}
			es = append(es, event{p1, i, 1}, event{p2, i, -1})
		}
	}
	sort.Sort(es)
	s := []int{}
	for _, e := range es {
		if e.d == 1 {
			s = append(s, e.i)
		} else {
			if s[len(s)-1] != e.i {
				Fprint(_w, "NO")
				return
			}
			s = s[:len(s)-1]
		}
	}
	Fprint(_w, "YES")
}

func main() { run(os.Stdin, os.Stdout) }