Escape

You are given an undirected graph whose vertices carry positive values. The vertices are numbered from 1 to $N$, and the $i$-th vertex has value $w_i$. You start at vertex 1 and may move around the graph under the constraint that you cannot traverse the edge you just came from. At each vertex, you gain points equal to that vertex's value, but only the first time you visit it.

Find the maximum total number of points you can obtain.

The input is given from standard input in the following format.

$N$ $M$

$w_1$ $w_2$ $...$ $w_N$

$u_1$ $v_1$

$u_2$ $v_2$

$...$

$u_M$ $v_M$

The first line contains the number of vertices $N$ and the number of edges $M$ of the graph. The second line contains the value $w_i$ of each vertex. The following $M$ lines each contain the numbers of the two vertices connected by an edge.

Output the answer on one line.

• $1 \leq N \leq 100000$
• $N-1 \leq M \leq 100000$
• $1 \leq w_i \leq 1000$
• $1 \leq u_i, v_i \leq N$
• There are no multiple edges or self-loops
• The graph is connected