p03685 AtCoder Regular Contest 076 - Connected?_16125
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.

Examples

Input

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


Output

YES


Input

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


Output

NO


Input

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


Output

YES


Input

1 1 2
0 0 1 1
1 0 0 1


Output

NO
import sys

def main():
    # res = []
    inps = map(lambda s: s.strip(), sys.stdin.readlines())
    iid = 0
    r, c, n = map(int, inps[iid].split())
    iid += 1

    def boundary(x,y):
        if x==0 or y==0 or x==r or y==c:
            return True
        return False

    def downright(x, y):
        if x==0 or y==c:
            return True
        return False


    points = []
    dr = []
    ul = []
    for i in xrange(1,n+1):
        x1, y1, x2, y2 = map(int, inps[iid].split())
        iid += 1
        if boundary(x1, y1) and boundary(x2, y2):
            if downright(x1,y1):
                dr.append((x1,y1,i))
            else:
                ul.append((x1,y1,i))
            if downright(x2,y2):
                dr.append((x2,y2,i))
            else:
                ul.append((x2,y2,i))
    dr.sort()
    ul.sort(reverse=True)
    dr.extend(ul)
    # print dr
    stack = []
    for elem in dr:
        if len(stack)!=0 and stack[-1]==elem[2]:
            stack.pop()
        else:
            stack.append(elem[2])
    if len(stack)==0:
        print "YES"
    else:
        print "NO"

    # print '\n'.join(res)
if __name__ == '__main__':
    main()