103354: [Atcoder]ABC335 E - Non-Decreasing Colorful Path

Problem Statement

There is a connected undirected graph with $N$ vertices and $M$ edges, where the $i$-th edge connects vertex $U_i$ and vertex $V_i$ bidirectionally.
Each vertex has an integer written on it, with integer $A_v$ written on vertex $v$.

For a simple path from vertex $1$ to vertex $N$ (a path that does not pass through the same vertex multiple times), the score is determined as follows:

• Let $S$ be the sequence of integers written on the vertices along the path, listed in the order they are visited.
• If $S$ is not non-decreasing, the score of that path is $0$.
• Otherwise, the score is the number of distinct integers in $S$.

Find the path from vertex $1$ to vertex $N$ with the highest score among all simple paths and print that score.

Constraints

• All input values are integers.
• $2 \le N \le 2 \times 10^5$
• $N-1 \le M \le 2 \times 10^5$
• $1 \le A_i \le 2 \times 10^5$
• The graph is connected.
• $1 \le U_i < V_i \le N$
• $(U_i,V_i) \neq (U_j,V_j)$ if $i \neq j$.

Input

The input is given from Standard Input in the following format:

$N$ $M$
$A_1$ $A_2$ $\dots$ $A_N$
$U_1$ $V_1$
$U_2$ $V_2$
$\vdots$
$U_M$ $V_M$

Output

Print the answer as an integer.

Sample Input 1

5 6
10 20 30 40 50
1 2
1 3
2 5
3 4
3 5
4 5

Sample Output 1

4

The path $1 \rightarrow 3 \rightarrow 4 \rightarrow 5$ has $S=(10,30,40,50)$ for a score of $4$, which is the maximum.

Sample Input 2

4 5
1 10 11 4
1 2
1 3
2 3
2 4
3 4

Sample Output 2

0

There is no simple path from vertex $1$ to vertex $N$ such that $S$ is non-decreasing. In this case, the maximum score is $0$.

Sample Input 3

10 12
1 2 3 3 4 4 4 6 5 7
1 3
2 9
3 4
5 6
1 2
8 9
4 5
8 10
7 10
4 6
2 8
6 7

Sample Output 3

5