N=int(input())
A=list(map(int,input().split()))
G=[[] for i in range(N)]
for i in range(N-1):
  a,b=map(int,input().split())
  G[a-1].append(b-1)
  G[b-1].append(a-1)
p=[[0]*N for i in range(20)]
dist=[-1]*N
from collections import deque
S=deque()
S.append(0)
dist[0]=0
while S:
  x=S.pop()
  for y in G[x]:
    if dist[y]>=0:
      continue
    dist[y]=dist[x]+1
    p[0][y]=x
    S.append(y)
for k in range(1,20):
  for i in range(N):
    p[k][i]=p[k-1][p[k-1][i]]
def LCA(a,b):
  x=a
  y=b
  if dist[x]>dist[y]:
    x,y=y,x
  u=dist[y]-dist[x]
  for k in range(20):
    if (u>>k)&1:
      y=p[k][y]
  if x==y:
    return x
  for k in range(19,-1,-1):
    if p[k][x]!=p[k][y]:
      x=p[k][x]
      y=p[k][y]
  y=p[0][y]
  return y
T={}
B=set()
for i in range(N):
  B.add(A[i])
B=list(B)
B.sort()
M=len(B)
for i in range(M):
  T[B[i]]=i
R=[[] for i in range(M)]
for i in range(N):
  R[T[A[i]]].append(i)
result=[0]*N
pos1=-1
pos2=-1
z=0
for i in range(M-1,-1,-1):
  for y in R[i]:
    if pos1==-1:
      pos1=y
    elif pos2==-1:
      pos2=y
      l=LCA(pos1,pos2)
      d=dist[pos1]+dist[pos2]-2*dist[l]
      z=d
      result[y]=d
    else:
      l1=LCA(pos1,y)
      l2=LCA(pos2,y)
      d1=dist[pos1]+dist[y]-2*dist[l1]
      d2=dist[pos2]+dist[y]-2*dist[l2]
      result[y]=max(d1,d2)
      if max(d1,d2)>z:
        z=max(d1,d2)
        if d1>=d2:
          pos2=y
        else:
          pos1=y
  if len(R[i])>1:
    for y in R[i]:
      l1=LCA(pos1,y)
      l2=LCA(pos2,y)
      d1=dist[pos1]+dist[y]-2*dist[l1]
      d2=dist[pos2]+dist[y]-2*dist[l2]
      result[y]=max(d1,d2)
      if max(d1,d2)>z:
        z=max(d1,d2)
        if d1>=d2:
          pos2=y
        else:
          pos1=y
print(*result)