Description

Input

The first line contains a single integer $n$ ($2 \le n \le 3 \cdot 10^5$) — the number of vertices in the tree.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2$) — the colors of the vertices. $a_i = 1$ means that vertex $i$ is colored red, $a_i = 2$ means that vertex $i$ is colored blue and $a_i = 0$ means that vertex $i$ is uncolored.

The $i$-th of the next $n - 1$ lines contains two integers $v_i$ and $u_i$ ($1 \le v_i, u_i \le n$, $v_i \ne u_i$) — the edges of the tree. It is guaranteed that the given edges form a tree. It is guaranteed that the tree contains at least one red vertex and at least one blue vertex.

Output

Print a single integer — the number of nice edges in the given tree.

Samples

5
2 0 0 1 2
1 2
2 3
2 4
2 5

1

5
1 0 0 0 2
1 2
2 3
3 4
4 5

4

3
1 1 2
2 3
1 3

0

Note

Here is the tree from the first example:

The only nice edge is edge $(2, 4)$. Removing it makes the tree fall apart into components $\{4\}$ and $\{1, 2, 3, 5\}$. The first component only includes a red vertex and the second component includes blue vertices and uncolored vertices.

Here is the tree from the second example:

Every edge is nice in it.

Here is the tree from the third example:

Edge $(1, 3)$ splits the into components $\{1\}$ and $\{3, 2\}$, the latter one includes both red and blue vertex, thus the edge isn't nice. Edge $(2, 3)$ splits the into components $\{1, 3\}$ and $\{2\}$, the former one includes both red and blue vertex, thus the edge also isn't nice. So the answer is 0.