Problem Description

This is a template problem.

Given a graph where each edge has a capacity and a cost, using each unit of flow through an edge incurs a specific cost. Given a source node $1$ and a sink node $n$, find the maximum flow in the graph and the minimum cost required for the maximum flow.

Input Format

The first line contains two integers $n$ and $m$, representing $n$ nodes and $m$ edges.

The following $m$ lines each contain four integers $s_i$, $t_i$, $c_i$, $w_i$, representing an edge from node $s_i$ to node $t_i$, with capacity $c_i$ and a unit flow cost of $w_i$.

Output Format

Output two integers: the maximum flow and the minimum cost required for the maximum flow.

Sample Input

8 23
2 3 2147483647 1
1 3 1 1
2 4 2147483647 2
1 4 1 2
2 8 2 0
3 5 2147483647 3
1 5 1 3
3 6 2147483647 4
1 6 1 4
3 8 2 0
3 2 2147483647 0
4 6 2147483647 5
1 6 1 5
4 7 2147483647 6
1 7 1 6
4 8 2 0
4 2 2147483647 0
5 8 0 0
5 2 2147483647 0
6 8 0 0
6 2 2147483647 0
7 8 0 0
7 2 2147483647 0

Sample Output

6 24

Data Constraints and Hints

• $1 \leq n \leq 400, 0 \leq m \leq 15000, w_i \geq 0$
• The input data, intermediate results, and the final answer are guaranteed to fit within a 32-bit signed integer.