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.