#pragma GCC target("avx")
//#pragma GCC target("avx512f,avx512dq,avx512cd,avx512bw,avx512vl")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#define LL long long
#define DB double
#define ST string
#define BS bitset
#define PA pair<LL,LL>
#define VE vector
#define VL vector<LL>
#define VP vector<pair<LL,LL>>
#define VVL vector<vector<LL>>
#define PQ priority_queue
#define PQS priority_queue<LL,vector<LL>,greater<LL>>
#define PB push_back
#define POB pop_back
#define PF push_front
#define POF pop_front
#define EB emplace_back
#define TS to_string
#define TU to_ullong
#define BPL __builtin_popcountll
#define FOR(i,a,n) for(i=a;i<n;i++)
#define FORR(i,a,n) for(i=n-1;i>=a;i--)
#define rep(i,n) FOR(i,0,n)
#define repr(i,n) FOR(i,0,n)
#define ALL(a) a.begin(),a.end()
#define RALL(a) a.rbegin(),a.rend()
#define SORT(a) sort(ALL(a))
#define REV(a) reverse(ALL(a))
#define UB(a,n) *upper_bound(ALL(a),n)
#define LB(a,n) *lower_bound(ALL(a),n)
#define INF 1145141919810364364
#define PI 3.14159265358979
#define MOD 1000000007
//#define MOD 998244353
#define ERR 0.00000001
//#define ERR 0.00000000000001
#define NUM 200010
#define FAST cin.tie(0);ios::sync_with_stdio(false)

void Yn(LL a){if(a)printf("Yes\n");else printf("No\n");}
void YN(LL a){if(a)printf("YES\n");else printf("NO\n");}
LL pwmn(LL a,LL n){LL ans=1;while(ans<a)ans*=n;return ans;}
LL dig(LL n){LL ret=0;while(n)n/=10,ret++;return ret;}
LL LBn(VL &v,LL a){LL mx=v.size(),mn=-1,md;while(mx-mn>1){md=(mx+mn)/2;if(v[md]<a)mn=md;else mx=md;}return mx;}
LL GCD(LL a,LL b){LL c=1,tmp=max(a,b);b=min(a,b);a=tmp;while(c!=0){c=a%b;a=b;b=c;}return a;}
LL LCM(LL a,LL b){return a*b/GCD(a,b);}
int lcmp(const void* a,const void* b){if(*(LL*)a>*(LL*)b)return 1;if(*(LL*)a<*(LL*)b)return -1;return 0;}
int lcmpr(const void* a,const void* b){if(*(LL*)a>*(LL*)b)return -1;if(*(LL*)a<*(LL*)b)return 1;return 0;}
int ccmp(const void* a,const void* b){return *(char*)a-*(char*)b;}
int ccmpr(const void* a,const void* b){return *(char*)b-*(char*)a;}
int scmp(const void* a,const void* b){return strcmp((char*)a,(char*)b);}
int scmpr(const void* a,const void* b){return strcmp((char*)b,(char*)a);}
LL mod(LL a,LL m){if(a%m<0)return a%m+m;else return a%m;}
LL DIV(LL a,LL d){LL m=MOD,x=1,y=0,k;while(m){k=d/m;d-=k*m;swap(m,d);x-=k*y;swap(x,y);}return mod(a*mod(x,MOD),MOD);}
LL POW(LL a,LL n){LL ans=1;while(n>0){if(n&1)ans=ans*a%MOD;a=a*a%MOD;n>>=1;}return ans;}
LL fact[NUM],finv[NUM],inv[NUM];
void comi(){LL i;fact[0]=fact[1]=1;finv[0]=finv[1]=1;inv[1]=1;FOR(i,2,NUM){fact[i]=fact[i-1]*i%MOD;inv[i]=MOD-inv[MOD%i]*(MOD/i)%MOD;finv[i]=finv[i-1]*inv[i]%MOD;}}
LL com(LL n,LL k){if(n<k||n<0||k<0)return 0;return fact[n]*(finv[k]*finv[n-k]%MOD)%MOD;}
bool cmps(pair<LL,LL> a,pair<LL,LL> b){if(a.second!=b.second)return a.second<b.second;return a.first<b.first;}
template<typename T>bool chmax(T &a,T b){if(a<b){a=b;return true;}return false;}
template<typename T>bool chmin(T &a,T b){if(a>b){a=b;return true;}return false;}

LL N;
VL dp,a,ans;
VVL t;
stack<PA> s;
void DFS(LL v,LL p){
  LL n=LBn(dp,a[v]);
  PA q;
  if(dp.size()==n){
    s.push({n,INF});
    dp.PB(a[v]);
  }else{
    s.push({n,dp[n]});
    dp[n]=a[v];
  }
  /*PA l;
  l=s.top();
  cout<<v<<" "<<dp.size()<<" "<<l.first<<" "<<l.second<<endl;*/
  ans[v]=dp.size();
  for(LL i:t[v])if(i!=p)DFS(i,v);
  if(!s.empty()){
    q=s.top();
    s.pop();
    if(q.second==INF)dp.POB();
    else dp[q.first]=q.second;
    //cout<<v<<" "<<q.first<<" "<<q.second<<endl;
  }
  /*for(LL r:dp)cout<<" "<<r;
  cout<<endl;*/
}

int main(){
  FAST;
  LL i,N,u,v;
  cin>>N;
  t.resize(N);
  a.resize(N);
  ans.resize(N);
  rep(i,N)cin>>a[i];
  rep(i,N-1){
    cin>>u>>v;
    u--,v--;
    t[u].PB(v);
    t[v].PB(u);
  }
  DFS(0,-1);
  rep(i,N)cout<<ans[i]<<endl;
}


Measured memory_bytes: 37380