CF1523F.Favorite Game

普及/提高-

通过率：0%

AC君温馨提醒

该题目为【codeforces】题库的题目，您提交的代码将被提交至codeforces进行远程评测，并由ACGO抓取测评结果后进行展示。由于远程测评的测评机由其他平台提供，我们无法保证该服务的稳定性，若提交后无反应，请等待一段时间后再进行重试。

题目描述

After William is done with work for the day, he enjoys playing his favorite video game.

The game happens in a 2D world, starting at turn $0$ . William can pick any cell in the game world and spawn in it. Then, each turn, William may remain at his current location or move from the current location (x, y) to one of the following locations: (x + 1, y), (x - 1, y), (x, y + 1), (x, y - 1).

To accelerate movement the game has $n$ fast travel towers. $i$ -th tower is located at location ( $xa_i, ya_i$ ). To be able to instantly travel to the tower from any location in the game world it must first be activated. Activation of tower $i$ happens at the moment when the player is in cell ( $xa_i, ya_i$ ) after this the tower remains active throughout the entire game.

William also knows that the game has $m$ quests. $i$ -th quest can be completed instantly by being at location ( $xb_i, yb_i$ ) on turn $t_i$ .

William wants to find out the maximal number of quests he will be able to complete by optimally traversing the game world.

输入格式

The first line contains two integers $n$ and $m$ ( $0 \le n \le 14, 1 \le m \le 100$ ), which are the number of towers and the number of quests, respectively.

Each of the next $n$ lines contains two integers $xa_i, ya_i$ ( $1 \le xa_i, ya_i \le 10^6$ ), which are the coordinates of fast travel towers.

Each of the next $m$ lines contains two integers $xb_i$ , $yb_i$ and $t_i$ ( $1 \le xb_i, yb_i \le 10^6$ , $1 \le t_i \le 10^9$ ), which are the coordinates of quests and the turn at which it may be completed.

It is guaranteed that all locations in a test are different.

输出格式

Print a single number — the maximal number of quests William will be able to complete.

输入输出样例

输入#1

输出#1

说明/提示

In the first sample test one of the possible sequences of William's actions is as follows:

Spawn at $(3, 2)$
On turn $1$ move to $(4, 2)$
On turn $2$ move to $(5, 2)$ . By visiting this cell William activates tower number $3$ .
On turn $3$ move to $(5, 1)$ , where he waits for $1$ turn to complete the $2$ nd quest
On turn $5$ move to $(5, 2)$
On turn $6$ move to $(5, 3)$
On turn $7$ move to $(5, 4)$
On turn $8$ move to $(5, 5)$
On turn $9$ move to $(4, 5)$
On turn $10$ move to $(3, 5)$ . By moving to this location William will complete the $4$ th quest
On turn $10$ instantly move to an already activated fast travel tower at $(5, 2)$
On turn $11$ move to $(6, 2)$ . By moving to this location William will complete the $3$ rd quest
William will not be able to complete the quest number $1$ , because the tower at $(2, 3)$ was not activated

首页