Captain America

题意翻译

平面上有 $n$ 个点，第 $i$ 个点的坐标为 $(x_i, y_i)$。 每个点都要被涂色，涂成红色需要 $r$ 元，涂成蓝色需要 $b$ 元。 另外有 $m$ 个限制，每个限制有两种可能： `1 l d` 表示在直线 $x = l$ 上，涂成两种颜色的点的数量之差不超过 $d$。 `2 l d` 表示在直线 $y = l$ 上，涂成两种颜色的点的数量之差不超过 $d$。 要求构造出一种涂色方案使得满足所有限制且总花费最少，或判断无法构造。 $n,m \le 10^5$。

题目描述

Steve Rogers is fascinated with new vibranium shields S.H.I.E.L.D gave him. They're all uncolored. There are $ n $ shields in total, the $ i $ -th shield is located at point $ (x_{i},y_{i}) $ of the coordinate plane. It's possible that two or more shields share the same location. Steve wants to paint all these shields. He paints each shield in either red or blue. Painting a shield in red costs $ r $ dollars while painting it in blue costs $ b $ dollars. Additionally, there are $ m $ constraints Steve wants to be satisfied. The $ i $ -th constraint is provided by three integers $ t_{i} $ , $ l_{i} $ and $ d_{i} $ : - If $ t_{i}=1 $ , then the absolute difference between the number of red and blue shields on line $ x=l_{i} $ should not exceed $ d_{i} $ . - If $ t_{i}=2 $ , then the absolute difference between the number of red and blue shields on line $ y=l_{i} $ should not exceed $ d_{i} $ . Steve gave you the task of finding the painting that satisfies all the condition and the total cost is minimum.

输入输出格式

输入格式

The first line of the input contains two integers $ n $ and $ m $ ( $ 1<=n,m<=100000 $ ) — the number of shields and the number of constraints respectively. The second line contains two integers $ r $ and $ b $ ( $ 1<=r,b<=10^{9} $ ). The next $ n $ lines contain the shields coordinates. The $ i $ -th of these lines contains two integers $ x_{i} $ and $ y_{i} $ ( $ 1<=x_{i},y_{i}<=10^{9} $ ). The next $ m $ lines contain the constrains. The $ j $ -th of these lines contains three integers $ t_{j} $ , $ l_{j} $ and $ d_{j} $ ( $ 1<=t_{j}<=2,1<=l_{j}<=10^{9},0<=d_{j}<=n $ ).

输出格式

If satisfying all the constraints is impossible print -1 in first and only line of the output. Otherwise, print the minimum total cost in the first line of output. In the second line print a string of length $ n $ consisting of letters 'r' and 'b' only. The $ i $ -th character should be 'r' if the $ i $ -th shield should be painted red in the optimal answer and 'b' if it should be painted blue. The cost of painting shields in these colors should be equal the minimum cost you printed on the first line. If there exist more than one optimal solution, print any of them.

输入输出样例

输入样例 #1

5 6
8 3
2 10
1 5
9 10
9 10
2 8
1 9 1
1 2 1
2 10 3
2 10 2
1 1 1
2 5 2

输出样例 #1

25
rbrbb

输入样例 #2

4 4
7 3
10 3
9 8
10 3
2 8
2 8 0
2 8 0
1 2 0
1 9 0

输出样例 #2

-1

题意翻译

平面上有 $n$ 个点，第 $i$ 个点的坐标为 $(x_i, y_i)$。 每个点都要被涂色，涂成红色需要 $r$ 元，涂成蓝色需要 $b$ 元。 另外有 $m$ 个限制，每个限制有两种可能： `1 l d` 表示在直线 $x = l$ 上，涂成两种颜色的点的数量之差不超过 $d$。 `2 l d` 表示在直线 $y = l$ 上，涂成两种颜色的点的数量之差不超过 $d$。 要求构造出一种涂色方案使得满足所有限制且总花费最少，或判断无法构造。 $n,m \le 10^5$。