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



Sample input:
4 2 3
0 1 3 1
1 1 4 1
2 0 2 2


Sample output:
YES

Submission status: Runtime Error

Solution code:
# coding: utf-8
import array, bisect, collections, copy, heapq, itertools, math, random, re, string, sys, time
sys.setrecursionlimit(10 ** 7)
INF = 10 ** 20
MOD = 10 ** 9 + 7


def II(): return int(input())
def ILI(): return list(map(int, input().split()))
def IAI(LINE): return [ILI() for __ in range(LINE)]
def IDI(): return {key: value for key, value in ILI()}


def read():
    R, C, N = ILI()
    num_point = []
    for __ in range(N):
        x_1, y_1, x_2, y_2 = ILI()
        num_point.append([(x_1, y_1), (x_2, y_2)])
    return R, C, N, num_point


# 周上を (0, 0) を原点として反時計回りに 1 本の数直線とした時の point の座標を返す．
# 周上にあるかの判定も行う．
def change_edge_point(R, C, point):
    x, y = point
    if 0 < x < C and 0 < y < R:
        return False
    if y == 0:
        return x
    elif y == R:
        return C + R + C - x
    if x == 0:
        return C + y
    elif x == R:
        return C + R + C + R - y


def solve(R, C, N, num_point):
    point_double = []
    for point in num_point:
        p_1, p_2 = point
        ret_1 = change_edge_point(R, C, p_1)
        ret_2 = change_edge_point(R, C, p_2)
        if ret_1 is False or ret_2 is False:
            continue
        point_double.append((min(ret_1, ret_2), max(ret_1, ret_2)))

    for p_1, p_2 in itertools.combinations(point_double, 2):
        if p_1[0] == p_2[0] or p_1[1] == p_2[1]:
            return "NO"

        if p_1[0] < p_2[0]:
            if p_1[1] > p_2[1]:
                continue
            else:
                return "NO"
        elif p_1[0] > p_2[0]:
            if p_1[1] < p_2[1]:
                continue
            else:
                return "NO"

    return "YES"


def main():
    params = read()
    print(solve(*params))


if __name__ == "__main__":
    main()

Submission status: Runtime Error

Solution code:
# coding: utf-8
import array, bisect, collections, copy, heapq, itertools, math, random, re, string, sys, time
sys.setrecursionlimit(10 ** 7)
INF = 10 ** 20
MOD = 10 ** 9 + 7


def II(): return int(input())
def ILI(): return list(map(int, input().split()))
def IAI(LINE): return [ILI() for __ in range(LINE)]
def IDI(): return {key: value for key, value in ILI()}


def read():
    R, C, N = ILI()
    num_point = []
    for __ in range(N):
        x_1, y_1, x_2, y_2 = ILI()
        num_point.append([(x_1, y_1), (x_2, y_2)])
    return R, C, N, num_point


# 周上を (0, 0) を原点として反時計回りに 1 本の数直線とした時の point の座標を返す．
# 周上にあるかの判定も行う．
def change_edge_point(R, C, point):
    x, y = point
    if 0 < x < C and 0 < y < R:
        return False
    if y == 0:
        return x
    elif y == R:
        return C + R + C - x
    if x == 0:
        return C + y
    elif x == R:
        return C + R + C + R - y


def solve(R, C, N, num_point):
    point_double = []
    for point in num_point:
        print(point)
        p_1, p_2 = point
        ret_1 = change_edge_point(R, C, p_1)
        ret_2 = change_edge_point(R, C, p_2)
        print(ret_1)
        print(ret_2)
        if ret_1 is False or ret_2 is False:
            continue
        point_double.append((min(ret_1, ret_2), max(ret_1, ret_2)))

    for p_1, p_2 in itertools.combinations(point_double, 2):
        if p_1[0] == p_2[0] or p_1[1] == p_2[1]:
            return "NO"

        if p_1[0] < p_2[0]:
            if p_1[1] > p_2[1]:
                continue
            else:
                return "NO"
        elif p_1[0] > p_2[0]:
            if p_1[1] < p_2[1]:
                continue
            else:
                return "NO"

    return "YES"


def main():
    params = read()
    print(solve(*params))


if __name__ == "__main__":
    main()

Submission status: Runtime Error

Solution code:
# coding: utf-8
import array, bisect, collections, copy, heapq, itertools, math, random, re, string, sys, time
sys.setrecursionlimit(10 ** 7)
INF = 10 ** 20
MOD = 10 ** 9 + 7


def II(): return int(input())
def ILI(): return list(map(int, input().split()))
def IAI(LINE): return [ILI() for __ in range(LINE)]
def IDI(): return {key: value for key, value in ILI()}


def read():
    R, C, N = ILI()
    num_point = []
    for __ in range(N):
        x_1, y_1, x_2, y_2 = ILI()
        num_point.append([(x_1, y_1), (x_2, y_2)])
    return R, C, N, num_point


# 周上を (0, 0) を原点として反時計回りに 1 本の数直線とした時の point の座標を返す．
# 周上にあるかの判定も行う．
def change_edge_point(R, C, point):
    x, y = point
    if 0 < x < C and 0 < y < R:
        return False
    if y == 0:
        return x
    elif y == R:
        return C + R + C - x
    if x == 0:
        return C + R + C + R - y
    elif x == R:
        return C + y


def solve(R, C, N, num_point):
    point_double = []
    for point in num_point:
        p_1, p_2 = point
        ret_1 = change_edge_point(R, C, p_1)
        ret_2 = change_edge_point(R, C, p_2)
        if ret_1 is False or ret_2 is False:
            continue
        point_double.append((ret_1, ret_2))

    for p_1, p_2 in itertools.combinations(point_double, 2):
        if p_1[0] == p_2[0] or p_1[1] == p_2[1]:
            return "NO"

        if p_1[0] < p_2[0]:
            if p_1[1] > p_2[1]:
                continue
            else:
                return "NO"
        elif p_1[0] > p_2[0]:
            if p_1[1] < p_2[1]:
                continue
            else:
                return "NO"

    return "YES"


def main():
    params = read()
    print(solve(*params))


if __name__ == "__main__":
    main()