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.

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.

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.

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.

见题面 Input 部分

见题面 Output 部分