Consider a tree with $n$ vertices, where each vertex is assigned either a white or black color. We want to determine the count of vertices, denoted as $u$, on the simple path from vertex $1$ to vertex $u$, where the number of white vertices exceeds the number of black vertices.
### Input
- The first line contains an integers $n$.
- The second line contains a binary string of length $n$, denoting the color of $n$ vertices. The $i^{th}$ character is the color of vertex $i$. $1$ is black and $0$ is white.
- The next $n - 1$ lines, each line contains two integers $u,v$, there is an edge between $u$ and $v$.
### Output
- Print the satisfied vertices.
### Constraints
- $1 \le n \le 10^5$.
- $1 \le u, v \le n$.
### Example
Input:
```
4
0110
1 2
2 3
2 4
```
Output:
```
2
```
