Buggy python submission (verdict: Runtime Error):
from bisect import bisect_left
from collections import deque
import sys

sys.setrecursionlimit(20000)

N = int(input())

a = list(map(int,input().split()))

graph = [[] for _ in range(N)]

for _ in range(N-1):
    u,v = map(int,input().split())
    u -= 1
    v -= 1
    graph[u].append(v)
    graph[v].append(u)

INF = 10**11
ans = [0]*N
dp = []###INFは空欄として扱って良い
stack = deque([])

def LISonTree(num,pre):
    ###num: 頂点番号
    ###pre: 1つ前にいた頂点番号
    p = bisect_left(dp,a[num])

    ###
    #print(p)
    ###

    if p >= len(dp):
        stack.appendleft((len(dp),INF))
        dp.append(a[num])
    else:
        stack.appendleft((p,dp[p]))
        dp[p] = a[num]
    
    q = bisect_left(dp,INF)
    ans[num] = q

    ###
    #print(num,'dp',dp)
    #print(num,'ans',ans)
    ###

    for x in graph[num]:
        if x == pre:
            continue
        LISonTree(x,num)
    
    changed_p, changed_v = stack.popleft()

    dp[changed_p] = changed_v

    ###
    #print(num,'dp',dp)
    ###

LISonTree(0,-1)
#print(ans)

for y in ans:
    print(y)

Fixed submission:
from bisect import bisect_left
from collections import deque
import sys

sys.setrecursionlimit(200001)

N = int(input())

a = list(map(int,input().split()))

graph = [[] for _ in range(N)]

for _ in range(N-1):
    u,v = map(int,input().split())
    u -= 1
    v -= 1
    graph[u].append(v)
    graph[v].append(u)

INF = 10**11
ans = [0]*N
dp = []###INFは空欄として扱って良い
stack = deque([])

def LISonTree(num,pre):
    ###num: 頂点番号
    ###pre: 1つ前にいた頂点番号
    p = bisect_left(dp,a[num])

    ###
    #print(p)
    ###

    if p >= len(dp):
        stack.appendleft((len(dp),INF))
        dp.append(a[num])
    else:
        stack.appendleft((p,dp[p]))
        dp[p] = a[num]
        
    
    q = bisect_left(dp,INF)
    ans[num] = q

    ###
    #print(num,'dp',dp)
    #print(num,'ans',ans)
    ###

    for x in graph[num]:
        if x == pre:
            continue
        LISonTree(x,num)
    
    changed_p, changed_v = stack.popleft()

    dp[changed_p] = changed_v

    ###
    #print(num,'dp',dp)
    ###

LISonTree(0,-1)
#print(ans)

for y in ans:
    print(y)

Buggy python submission (verdict: Runtime Error):
from bisect import bisect_left
from collections import deque
import sys

sys.setrecursionlimit(10000)

N = int(input())

a = list(map(int,input().split()))

graph = [[] for _ in range(N)]

for _ in range(N-1):
    u,v = map(int,input().split())
    u -= 1
    v -= 1
    graph[u].append(v)
    graph[v].append(u)

INF = 10**11
ans = [0]*N
dp = []###INFは空欄として扱って良い
stack = deque([])

def LISonTree(num,pre):
    ###num: 頂点番号
    ###pre: 1つ前にいた頂点番号
    p = bisect_left(dp,a[num])

    ###
    #print(p)
    ###

    if p >= len(dp):
        stack.appendleft((len(dp),INF))
        dp.append(a[num])
    else:
        stack.appendleft((p,dp[p]))
        dp[p] = a[num]
    
    q = bisect_left(dp,INF)
    ans[num] = q

    ###
    #print(num,'dp',dp)
    #print(num,'ans',ans)
    ###

    for x in graph[num]:
        if x == pre:
            continue
        LISonTree(x,num)
    
    changed_p, changed_v = stack.popleft()

    dp[changed_p] = changed_v

    ###
    #print(num,'dp',dp)
    ###

LISonTree(0,-1)
#print(ans)

for y in ans:
    print(y)

Fixed submission:
from bisect import bisect_left
from collections import deque
import sys

sys.setrecursionlimit(200001)

N = int(input())

a = list(map(int,input().split()))

graph = [[] for _ in range(N)]

for _ in range(N-1):
    u,v = map(int,input().split())
    u -= 1
    v -= 1
    graph[u].append(v)
    graph[v].append(u)

INF = 10**11
ans = [0]*N
dp = []###INFは空欄として扱って良い
stack = deque([])

def LISonTree(num,pre):
    ###num: 頂点番号
    ###pre: 1つ前にいた頂点番号
    p = bisect_left(dp,a[num])

    ###
    #print(p)
    ###

    if p >= len(dp):
        stack.appendleft((len(dp),INF))
        dp.append(a[num])
    else:
        stack.appendleft((p,dp[p]))
        dp[p] = a[num]
        
    
    q = bisect_left(dp,INF)
    ans[num] = q

    ###
    #print(num,'dp',dp)
    #print(num,'ans',ans)
    ###

    for x in graph[num]:
        if x == pre:
            continue
        LISonTree(x,num)
    
    changed_p, changed_v = stack.popleft()

    dp[changed_p] = changed_v

    ###
    #print(num,'dp',dp)
    ###

LISonTree(0,-1)
#print(ans)

for y in ans:
    print(y)

Buggy python submission (verdict: Runtime Error):
from bisect import bisect_left
from collections import deque

N = int(input())

a = list(map(int,input().split()))

graph = [[] for _ in range(N)]

for _ in range(N-1):
    u,v = map(int,input().split())
    u -= 1
    v -= 1
    graph[u].append(v)
    graph[v].append(u)

INF = 10**11
ans = [0]*N
dp = []###INFは空欄として扱って良い
stack = deque([])

def LISonTree(num,pre):
    ###num: 頂点番号
    ###pre: 1つ前にいた頂点番号
    p = bisect_left(dp,a[num])

    ###
    #print(p)
    ###

    if p >= len(dp):
        stack.appendleft((len(dp),INF))
        dp.append(a[num])
    else:
        stack.appendleft((p,dp[p]))
        dp[p] = a[num]
    
    q = bisect_left(dp,INF)
    ans[num] = q

    ###
    #print(num,'dp',dp)
    #print(num,'ans',ans)
    ###

    for x in graph[num]:
        if x == pre:
            continue
        LISonTree(x,num)
    
    changed_p, changed_v = stack.popleft()

    dp[changed_p] = changed_v

    ###
    #print(num,'dp',dp)
    ###

LISonTree(0,-1)
#print(ans)

for y in ans:
    print(y)

Fixed submission:
from bisect import bisect_left
from collections import deque
import sys

sys.setrecursionlimit(200001)

N = int(input())

a = list(map(int,input().split()))

graph = [[] for _ in range(N)]

for _ in range(N-1):
    u,v = map(int,input().split())
    u -= 1
    v -= 1
    graph[u].append(v)
    graph[v].append(u)

INF = 10**11
ans = [0]*N
dp = []###INFは空欄として扱って良い
stack = deque([])

def LISonTree(num,pre):
    ###num: 頂点番号
    ###pre: 1つ前にいた頂点番号
    p = bisect_left(dp,a[num])

    ###
    #print(p)
    ###

    if p >= len(dp):
        stack.appendleft((len(dp),INF))
        dp.append(a[num])
    else:
        stack.appendleft((p,dp[p]))
        dp[p] = a[num]
        
    
    q = bisect_left(dp,INF)
    ans[num] = q

    ###
    #print(num,'dp',dp)
    #print(num,'ans',ans)
    ###

    for x in graph[num]:
        if x == pre:
            continue
        LISonTree(x,num)
    
    changed_p, changed_v = stack.popleft()

    dp[changed_p] = changed_v

    ###
    #print(num,'dp',dp)
    ###

LISonTree(0,-1)
#print(ans)

for y in ans:
    print(y)