human
Write me a Python code to find the length of the longest increasing subsequence of this sequence given the following:
I found an interesting problem on https://atcoder.jp/contests/abc165/tasks/abc165_f:
We have a tree with N vertices, whose i-th edge connects Vertex u_i and Vertex v_i.
Vertex i has an integer a_i written on it.
For every integer k from 1 through N, solve the following problem:
 - We will make a sequence by lining up the integers written on the vertices along the shortest path from Vertex 1 to Vertex k, in the order they appear. Find the length of the longest increasing subsequence of this sequence.
Here, the longest increasing subsequence of a sequence A of length L is the subsequence A_{i_1} , A_{i_2} , ... , A_{i_M} with the greatest possible value of M such that 1 \leq i_1 < i_2 < ... < i_M \leq L and A_{i_1} < A_{i_2} < ... < A_{i_M}.

-----Constraints-----
 - 2 \leq N \leq 2 \times 10^5
 - 1 \leq a_i \leq 10^9
 - 1 \leq u_i , v_i \leq N
 - u_i \neq v_i
 - The given graph is a tree.
 - All values in input are integers.

-----Input-----
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
u_1 v_1
u_2 v_2
:
u_{N-1} v_{N-1}

-----Output-----
Print N lines. The k-th line, print the length of the longest increasing subsequence of the sequence obtained from the shortest path from Vertex 1 to Vertex k.

-----Sample Input-----
10
1 2 5 3 4 6 7 3 2 4
1 2
2 3
3 4
4 5
3 6
6 7
1 8
8 9
9 10

-----Sample Output-----
1
2
3
3
4
4
5
2
2
3

For example, the sequence A obtained from the shortest path from Vertex 1 to Vertex 5 is 1,2,5,3,4. Its longest increasing subsequence is A_1, A_2, A_4, A_5, with the length of 4.

I tried it in Python, but could not do it. Can you solve it?
assistant
#Here is Python code to find the length of the longest increasing subsequence of this sequence.

# 写経
# https://atcoder.jp/contests/abc165/submissions/12655073
from bisect import bisect_left, bisect_right
import sys

def resolve():
    input = sys.stdin.readline
    sys.setrecursionlimit(10**9)
    INF = float('inf') 
    N = int(input())
    As = list(map(int, input().split()))
    adjL = [[] for _ in range(N)]
    for _ in range(N-1):
        u, v = map(int, input().split())
        u, v = u-1, v-1
        adjL[u].append(v)
        adjL[v].append(u)
    
    dp = [-INF]
    anss = [0] * N
    def dfs(vNow, vPar):
        A = As[vNow]
        if dp[-1] < A:
            dp.append(A)
            tp = 0
        else:
            i = bisect_left(dp, A)
            tp = 1
            iOld, AOld, = i, dp[i]
            dp[i] = A
        anss[vNow] = len(dp) - 1
    
        for v2 in adjL[vNow]:
            if v2 == vPar: continue
            dfs(v2, vNow)
    
        if tp == 0:
            dp.pop()
        else:
            dp[iOld] = AOld
    
    dfs(0, -1)

    print('\n'.join(map(str, anss)))
resolve()