Problem Statement

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 $S$.

Constraints

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

Input

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}

Output

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