Given a tree of $n$ vertices, vertex $i$ has integer $A_i$.
Find a subset of vertices $u_1,u_2,..,u_k$ so that for every pair $(i,j)$ that $1 \le i, j \le k$, if $u_i$ is an ancestor of $u_j$ then $A_{u_j} < A_{u_i}$.
### Input
- The first line contains an integer $n$.
- The second line contains $n$ integers $A_i$.
- The next $n$ lines, each line contains two integers $u, v$, there is an edge between $u$ and $v$.
### Output
- Print a single integer is the answer.
### Constraints
- $1 \le n \le 10^5$.
- $1 \le A_i \le 10^9$.
- $1 \le u, v \le n$.
### Example
Input:
```
4
1 4 2 3
1 2
2 3
2 4
```
Output:
```
3
```
