Score : $500$ points

问题描述

在 AtCoder 滑雪场有 $N$ 个开放区域，分别称为 Space $1$、Space $2$、$\ldots$、Space $N$。其中，Space $i$ 的海拔高度为 $H_i$。存在 $M$ 条双向连接两个空间的滑雪道。第 $i$ 条滑雪道（$1 \leq i \leq M$）连接了 Space $U_i$ 和 Space $V_i$。通过一些滑雪道，可以在任意两个空间之间穿梭。

高桥只能通过滑雪道在各空间之间移动。每次他经过一条滑雪道时，他的幸福感会发生变化。具体来说，当他通过直接相连的滑雪道从 Space $X$ 移动到 Space $Y$ 时，其幸福感的变化如下：

• 如果 Space $X$ 的海拔高于 Space $Y$，幸福感会增加两者之差：$H_X - H_Y$。
• 如果 Space $X$ 的海拔低于 Space $Y$，幸福感会减少两者之差的两倍：$2(H_Y - H_X)$。
• 如果 Space $X$ 的海拔等于 Space $Y$，幸福感不变。

幸福感可能为负值。

最初，高桥位于 Space $1$，且其幸福感为 $0$。请找出经过任意数量滑雪道（包括零条）后，以任意一个空间为终点时，他所能达到的最大幸福感。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

AtCoder Ski Area has $N$ open spaces called Space $1$, Space $2$, $\ldots$, Space $N$. The altitude of Space $i$ is $H_i$. There are $M$ slopes that connect two spaces bidirectionally. The $i$-th slope $(1 \leq i \leq M)$ connects Space $U_i$ and Space $V_i$. It is possible to travel between any two spaces using some slopes.

Takahashi can only travel between spaces by using slopes. Each time he goes through a slope, his happiness changes. Specifically, when he goes from Space $X$ to Space $Y$ by using the slope that directly connects them, his happiness changes as follows.

• If the altitude of Space $X$ is strictly higher than that of Space $Y$, the happiness increases by their difference: $H_X-H_Y$.
• If the altitude of Space $X$ is strictly lower than that of Space $Y$, the happiness decreases by their difference multiplied by $2$: $2(H_Y-H_X)$.
• If the altitude of Space $X$ is equal to that of Space $Y$, the happiness does not change.

The happiness may be a negative value.

Initially, Takahashi is in Space $1$, and his happiness is $0$. Find his maximum possible happiness after going through any number of slopes (possibly zero), ending in any space.

Constraints

• $2 \leq N \leq 2\times 10^5$
• $N-1 \leq M \leq \min( 2\times 10^5,\frac{N(N-1)}{2})$
• $0 \leq H_i\leq 10^8$ $(1 \leq i \leq N)$
• $1 \leq U_i < V_i \leq N$ $(1 \leq i \leq M)$
• $(U_i,V_i) \neq (U_j, V_j)$ if $i \neq j$.
• All values in input are integers.
• It is possible to travel between any two spaces using some slopes.

Input

Input is given from Standard Input in the following format:

$N$ $M$

$H_1$ $H_2$ $\ldots$ $H_N$

$U_1$ $V_1$

$U_2$ $V_2$

$\vdots$

$U_M$ $V_M$

Output

Print the answer.

Sample Input 1

4 4
10 8 12 5
1 2
1 3
2 3
3 4

Sample Output 1

3

If Takahashi takes the route Space $1$ $\to$ Space $3$ $\to$ Space $4$, his happiness changes as follows.

• When going from Space $1$ (altitude $10$) to Space $3$ (altitude $12$), it decreases by $2\times (12-10)=4$ and becomes $0-4=-4$.
• When going from Space $3$ (altitude $12$) to Space $4$ (altitude $5$), it increases by $12-5=7$ and becomes $-4+7=3$.

If he ends the travel here, the final happiness will be $3$, which is the maximum possible value.

Sample Input 2

2 1
0 10
1 2

Sample Output 2

0

His happiness is maximized by not moving at all.

update @ 2024/3/10 10:16:00