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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdio>
using namespace std;
typedef long long ll;
const ll maxn = 200000 + 10;

ll R, C, n, stk[maxn << 1], top = 0;
struct data{
  ll l, r;
  data() {}
  data(ll _l, ll _r):l(_l), r(_r) {}
  
  friend bool operator < (data a, data b) {
    return a.l < b.l;
	}
}a[maxn], b[maxn << 1];

int main() {
  scanf("%d%d%d", &R, &C, &n);
  R ++; C ++; ll tot = 0;
  for(ll i = 1;i <= n;i ++) {
    ll x1, y1, x2, y2;
    scanf("%d%d%d%d", &x1, &y1, &x2, &y2);
    x1 ++; x2 ++; y1 ++; y2 ++;
    if(x1 > x2) swap(x1,x2), swap(y1,y2);
    if(x1 == 1 && x2 == R) {
      a[++ tot] = data(R + C + C - y2 + 1,y1);
      continue;
		}
		if(y1 > y2) swap(x1,x2), swap(y1,y2);
		if(y1 == 1 && y2 == C) {
		  a[++ tot] = data(R + 2 * C + R - x1 + 1,C + x2); 
		  continue;
		}
		if(y2 == 1 && x1 == 1) swap(x1,x2), swap(y1,y2);
		if(y1 == 1 && x2 == 1) {
			a[++ tot] = data(R + 2 * C + R - x1 + 1,y2);
			continue;
		}
		if(y2 == 1 && x1 == R) swap(x1,x2), swap(y1,y2);
		if(y1 == 1 && x2 == R) {
		  a[++ tot] = data(R + 2 * C + R - x1 + 1,R + C + C - y2 + 1);
		  continue;
		}
		if(x2 == R && y1 == C) swap(x1,x2), swap(y1,y2);
		if(x1 == R && y2 == C) {
			a[++ tot] = data(R + C + C - y1 + 1,C + x2);
			continue;
		}
		if(x2 == 1 && y1 == C) swap(x1,x2), swap(y1,y2);
		if(x1 == 1 && y2 == C) {
			a[++ tot] = data(C + x2,y1);
			continue;
		}
		if(x1 == 1 && x2 == 1) {
		  a[++ tot] = data(y2,y1);
		  continue;
		}
		if(y1 == C && y2 == C) {
		  a[++ tot] = data(C + x2,C + x1);
		  continue;
		}
		if(x1 == R && x2 == R) {
		  a[++ tot] = data(R + C + C - y1 + 1,R + C + C - y2 + 1);
		  continue;
		}
		if(y1 == 1 && y2 == 1) {
		  a[++ tot] = data(R + 2 * C + R - x1 + 1,R + 2 * C + R - x2 + 1);
		  continue;
		}
	}
	for(int i = 1;i <= tot;i ++) if(a[i].l > a[i].r) swap(a[i].l,a[i].r); 
	ll cnt = 0;
	for(ll i = 1;i <= tot;i ++) {
	  b[++ cnt].l = a[i].l, b[cnt].r = i;
	  b[++ cnt].l = a[i].r, b[cnt].r = - i;
	}
	sort(b + 1,b + cnt + 1);
	top = 0;
	for(ll i = 1;i <= cnt;i ++) {
		if(b[i].r > 0) stk[++ top] = b[i].r;
		else {
		  if(stk[top] != - b[i].r) {
		    puts("NO");
		    return 0;
			}
			top --;
		}
	}
	if(top) puts("NO");
	else puts("YES");
  return 0;
}