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 ith 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≤n≤105.
- 1≤u,v≤n.
### Example
Input:
40110122324
Output:
2