##### Canadian Computing Competition: 2023 Stage 1, Senior #4

As the newly elected mayor of Kitchener, Alanna's first job is to improve the city's road plan.

Kitchener's current road plan can be represented as a collection of intersections with roads, where the -th road has length meters, costs dollars per year to maintain, and connects intersections and . To create a plan, Alanna must select some subset of the roads to keep and maintain, and that plan's cost is the sum of maintenance costs of all roads in that subset.

To lower the city's annual spending, Alanna would like to minimize the plan's cost. However, the city also requires that she minimizes travel distances between intersections and will reject any plan that does not conform to those rules. Formally, for any pair of intersections , if there exists a path from to taking meters on the existing road plan, Alanna's plan must also include a path between those intersections that is at most meters.

#### Input Specification

The first line contains the integers and .

Each of the next lines contains the integers , , , and , meaning that there currently exists a road from intersection to intersection with length and cost .

The following table shows how the available 15 marks are distributed:

Marks Awarded |
Bounds on and |
Bounds on |
Bounds on |
Additional Constraints |
---|---|---|---|---|

3 marks | None | |||

6 marks | There is at most one road between any unordered pair of intersections. | |||

6 marks | None |

#### Output Specification

Output one integer, the minimum possible cost of a road plan that meets the requirements.

#### Sample Input

```
5 7
1 2 15 1
2 4 9 9
5 2 5 6
4 5 4 4
4 3 3 7
1 3 2 7
1 4 2 1
```

#### Output for Sample Input

`25`

#### Explanation of Output for Sample Input

Here is a diagram of the intersections along with a valid road plan with minimum cost.

Each edge is labeled with a pair denoting that it has length meters and cost dollars. Additionally, the roads that are part of the plan are highlighted, with a total cost of .

It can be shown that we cannot create a cheaper plan that also respects the city's requirements.

## Comments

It seems that it's possible for two intersections to have multiple roads connecting them and that the entire initial road plan does not have to be connected. I spent way too long trying to fix those...