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, math, collections, heapq, itertools
F = sys.stdin
def single_input(): return F.readline().strip("\n")
def line_input(): return F.readline().strip("\n").split()

def solve():
    R, C, N = map(int, line_input())
    u, l, r, d = [], [], [], []
    for i in range(N):
        x, y, z, w = map(int, line_input())
        if x == 0:
            if z == 0: 
                u.append((y, i))
                u.append((w, i))
            elif w == C:
                u.append((y, i))
                r.append((z, i))
            elif z == R:
                u.append((y, i))
                d.append((w, i))
            elif w == 0:
                u.append((y, i))
                l.append((z, i))
        elif x == R:
            if z == 0: 
                d.append((y, i))
                u.append((w, i))
            elif w == C:
                d.append((y, i))
                r.append((z, i))
            elif z == R:
                d.append((y, i))
                d.append((w, i))
            elif w == 0:
                d.append((y, i))
                l.append((z, i))
        elif y == 0:
            if z == 0: 
                l.append((x, i))
                u.append((w, i))
            elif w == C:
                l.append((x, i))
                r.append((z, i))
            elif z == R:
                l.append((x, i))
                d.append((w, i))
            elif w == 0:
                l.append((x, i))
                l.append((z, i))
        elif y == C:
            if z == 0: 
                r.append((x, i))
                u.append((w, i))
            elif w == C:
                r.append((x, i))
                r.append((z, i))
            elif z == R:
                r.append((x, i))
                d.append((w, i))
            elif w == 0:
                r.append((x, i))
                l.append((z, i))
    u.sort()
    r.sort()
    d.sort(reverse = True)
    l.sort(reverse = True)

    s = []
    used = set()
    crossed = True
    for point, n in u:
        if n not in used:
            s.append(n)
            used |= {n}
        else:
            if s[-1] != n: break
            else: s.pop()
    else:
        for point, n in r:
            if n not in used:
                s.append(n)
                used |= {n}
            else:
                if s[-1] != n: break
                else: s.pop()
        else:
            for point, n in d:
                if n not in used:
                    s.append(n)
                    used |= {n}
                else:
                    if s[-1] != n: break
                    else: s.pop()
            else:
                for point, n in l:
                    if n not in used:
                        s.append(n)
                        used |= {n}
                    else:
                        if s[-1] != n: break
                        else: s.pop()
                else: crossed = False

    print("NO" if crossed else "YES")
                            
    return 0
  
if __name__ == "__main__":
    solve()