Jury Meeting

题意翻译

现在有(n+1)个城市，其中第1~n个城市每个城市有一个人，第0个城市是人们需要聚集的地方。还有m条航班，每条航班从0到其他城市或从其他城市到0，当天即可抵达，现在需要选定一个时间段，长度为k天，使得这一个时间段里人们都在0城市工作(航班抵达和离开0城市的那一天不能进行工作)，问把n个人送到0城市，工作完成后再送回去的最小花费。

题目描述

Country of Metropolia is holding Olympiad of Metrpolises soon. It mean that all jury members of the olympiad should meet together in Metropolis (the capital of the country) for the problem preparation process. There are $ n+1 $ cities consecutively numbered from $ 0 $ to $ n $ . City $ 0 $ is Metropolis that is the meeting point for all jury members. For each city from $ 1 $ to $ n $ there is exactly one jury member living there. Olympiad preparation is a long and demanding process that requires $ k $ days of work. For all of these $ k $ days each of the $ n $ jury members should be present in Metropolis to be able to work on problems. You know the flight schedule in the country (jury members consider themselves important enough to only use flights for transportation). All flights in Metropolia are either going to Metropolis or out of Metropolis. There are no night flights in Metropolia, or in the other words, plane always takes off at the same day it arrives. On his arrival day and departure day jury member is not able to discuss the olympiad. All flights in Megapolia depart and arrive at the same day. Gather everybody for $ k $ days in the capital is a hard objective, doing that while spending the minimum possible money is even harder. Nevertheless, your task is to arrange the cheapest way to bring all of the jury members to Metrpolis, so that they can work together for $ k $ days and then send them back to their home cities. Cost of the arrangement is defined as a total cost of tickets for all used flights. It is allowed for jury member to stay in Metropolis for more than $ k $ days.

输入输出格式

输入格式

The first line of input contains three integers $ n $ , $ m $ and $ k $ ( $ 1<=n<=10^{5} $ , $ 0<=m<=10^{5} $ , $ 1<=k<=10^{6} $ ). The $ i $ -th of the following $ m $ lines contains the description of the $ i $ -th flight defined by four integers $ d_{i} $ , $ f_{i} $ , $ t_{i} $ and $ c_{i} $ ( $ 1<=d_{i}<=10^{6} $ , $ 0<=f_{i}<=n $ , $ 0<=t_{i}<=n $ , $ 1<=c_{i}<=10^{6} $ , exactly one of $ f_{i} $ and $ t_{i} $ equals zero), the day of departure (and arrival), the departure city, the arrival city and the ticket cost.

输出格式

Output the only integer that is the minimum cost of gathering all jury members in city $ 0 $ for $ k $ days and then sending them back to their home cities. If it is impossible to gather everybody in Metropolis for $ k $ days and then send them back to their home cities, output "-1" (without the quotes).

输入输出样例

输入样例 #1

2 6 5
1 1 0 5000
3 2 0 5500
2 2 0 6000
15 0 2 9000
9 0 1 7000
8 0 2 6500

输出样例 #1

24500

输入样例 #2

2 4 5
1 2 0 5000
2 1 0 4500
2 1 0 3000
8 0 1 6000

输出样例 #2

-1

说明

The optimal way to gather everybody in Metropolis in the first sample test is to use flights that take place on days $ 1 $ , $ 2 $ , $ 8 $ and $ 9 $ . The only alternative option is to send jury member from second city back home on day $ 15 $ , that would cost 2500 more. In the second sample it is impossible to send jury member from city $ 2 $ back home from Metropolis.