201075: [AtCoder]ARC107 F - Sum of Abs

Problem Statement

Given is a simple undirected graph with $N$ vertices and $M$ edges. Its vertices are numbered $1, 2, \ldots, N$ and its edges are numbered $1, 2, \ldots, M$. On Vertex $i$ ($1 \leq i \leq N$) two integers $A_i$ and $B_i$ are written. Edge $i$ ($1 \leq i \leq M$) connects Vertices $U_i$ and $V_i$.

Snuke picks zero or more vertices and delete them. Deleting Vertex $i$ costs $A_i$. When a vertex is deleted, edges that are incident to the vertex are also deleted. The score after deleting vertices is calculated as follows:

• The score is the sum of the scores of all connected components.
• The score of a connected component is the absolute value of the sum of $B_i$ of the vertices in the connected component.

Snuke's profit is $($score$)$ $-$ $($the sum of costs$)$. Find the maximum possible profit Snuke can gain.

Constraints

• $1 \leq N \leq 300$
• $1 \leq M \leq 300$
• $1 \leq A_i \leq 10^6$
• $-10^6 \leq B_i \leq 10^6$
• $1 \leq U_i,V_i \leq N$
• The given graph does not contain self loops or multiple edges.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$
$A_1$ $A_2$ $\cdots$ $A_N$
$B_1$ $B_2$ $\cdots$ $B_N$
$U_1$ $V_1$
$U_2$ $V_2$
$\vdots$
$U_M$ $V_M$

Output

Print the maximum possible profit Snuke can gain.

Sample Input 1

4 4
4 1 2 3
0 2 -3 1
1 2
2 3
3 4
4 2

Sample Output 1

1

Deleting Vertex $2$ costs $1$. After that, the graph is separated into two connected components. The score of the component consisting of Vertex $1$ is $|0| = 0$. The score of the component consisting of Vertices $3$ and $4$ is $|(-3) + 1| = 2$. Therefore, Snuke's profit is $0 + 2 - 1 = 1$. He cannot gain more than $1$, so the answer is $1$.

Sample Input 2

10 12
733454 729489 956011 464983 822120 364691 271012 762026 751760 965431
-817837 -880667 -822819 -131079 740891 581865 -191711 -383018 273044 476880
3 1
4 1
6 9
3 8
1 6
10 5
5 6
1 5
4 3
7 1
7 4
10 3

Sample Output 2

2306209

Sample Input 3

4 2
1 1 1 1
1 1 -1 -1
1 2
3 4

Sample Output 3

4

The given graph is not necessarily connected.