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: Wrong Answer)

#include<stdio.h>
#include<iostream>
#include<algorithm>
#include<stdlib.h>
#include<string.h>
#include<queue>
#define LL long long
using namespace std;
inline int read( )
{
  int sum=0;char c=getchar( );bool f=0;
  while(c<'0'||c>'9') {if(c=='-') f=1;c=getchar( );}
  while(c>='0'&&c<='9') {sum=sum*10+c-'0';c=getchar( );}
  if(f) return -sum;
  return sum;
}
const int I1=1e8,I2=2e8,I3=3e8;
const int N=200005;
int R,C,n,m,st[N];
inline int ch(int x,int y)
{
  if(!x) return 1+y;
  if(y==C) return I1+x;
  if(x==R) return I2-y;
  if(!y) return I3-x;
  return 0;
}
struct ex{int p,v;}d[N];
inline bool operator < (const ex &a,const ex &b) {return a.p<b.p;}
int main( )
{
  int i,x1,y1,x2,y2,A,B;
  R=read( );C=read( );n=read( );
  for(i=1;i<=n;i++)
    {
      x1=read( );y1=read( );x2=read( );y2=read( );
      if((A=ch(x1,y1))&&(B=ch(x2,y2))) d[++m]=(ex){A,i},d[++m]=(ex){B,i};
    }
  sort(d+1,d+m+1);
  int top=0;
  for(i=1;i<=m;i++)
    {
      if(!top||st[top]!=d[i].v) st[++top]=d[i].v;
      else top--;
    }
  puts(top?"NO":"YES");
  return 0;
}