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 Pascal (FPC 2.6.2) (judge verdict: Runtime Error)

var
        m,i,j,a,b,c,d,x,y,n:longint;
        gtx,gty:real;
        xx1,xx2,xa,xb,xy1,xy2:array [0..1000000] of real;
function max(a,b:real):real;
        begin
        if a>b then exit(a);
        exit(b);
        end;
function min(a,b:real):real;
        begin
        if a>b then exit(b);
        exit(a);
        end;
function kt(var a,b:real; c,d:longint):boolean;
        begin
        if (max(xx1[c],xx2[c])>=a) and (min(xx1[c],xx2[c])<=a) and (max(xy1[c],xy2[c])>=b) and (min(xy1[c],xy2[c])<=b) then
                exit(true);
        if (max(xx1[d],xx2[d])>=a) and (min(xx1[d],xx2[d])<=a) and (max(xy1[d],xy2[d])>=b) and (min(xy1[d],xy2[d])<=b) then
                exit(true);
        exit(false);
        end;
begin
readln(x,y,n);
for i:=1 to n do
        begin
        readln(a,b,c,d);
        if ((a=x) or (a=0) or (b=y) or (b=0)) and ((c=x) or (c=0) or (d=y) or (d=0)) then
                if a<>c then
                        begin
                        inc(m);
                        xa[m]:=(b-d)/(a-c);
                        xb[m]:=b-a*xa[m];
                        xx1[m]:=a;
                        xy1[m]:=b;
                        xx2[m]:=c;
                        xy2[m]:=d;
                        end;
        end;
for i:=1 to m do
        for j:=i+1 to m do
                begin
                gtx:=-(xb[i]-xb[j])/(xa[i]-xa[j]);
                gty:=xa[i]*gtx+xb[i];
                if kt(gtx,gty,i,j) then
                        begin
                        writeln('NO');
                        halt;
                        end;
                end;
writeln('YES');
end.