There is a tree $T$ with $N$ vertices numbered from $1$ to $N$. The $i$-th edge connects vertices $u_i$ and $v_i$. Additionally, vertex $i$ is painted with color $A_i$.  
Find the number, modulo $998244353$, of (non-empty) subsets $S$ of the vertex set of $T$ that satisfy the following condition:

-   The induced subgraph $G$ of $T$ by $S$ satisfies all of the following conditions:
    -   $G$ is a tree.
    -   All vertices with degree $1$ have the same color.

What is an induced subgraph? Let $S$ be a subset of the vertices of a graph $G$. The induced subgraph of $G$ by $S$ is a graph whose vertex set is $S$ and whose edge set consists of all edges in $G$ that have both endpoints in $S$.

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

```
$N$
$A_1$ $A_2$ $\dots$ $A_N$
$u_1$ $v_1$
$u_2$ $v_2$
$\vdots$
$u_{N-1}$ $v_{N-1}$
```

Print the number, modulo $998244353$, of (non-empty) subsets $S$ of the vertex set of $T$ that satisfy the condition in the problem statement.

-   $1 \leq N \leq 2 \times 10^5$
-   $1 \leq A_i \leq N$
-   $1 \leq u_i \lt v_i \leq N$
-   The graph given in the input is a tree.
-   All input values are integers.

4

The following four sets of vertices satisfy the condition.

• {1}
• {1,2,3}
• {2}
• {3}