#include<bits/stdc++.h>
#include<atcoder/all>
#define rep(i,b) for(int i=0;i<b;i++)
#define rrep(i,b) for(int i=b-1;i>=0;i--)
#define rep1(i,b) for(int i=1;i<b;i++)
#define repx(i,x,b) for(int i=x;i<b;i++)
#define rrepx(i,x,b) for(int i=b-1;i>=x;i--)
#define fore(i,a) for(auto& i:a)
#define rng(x) (x).begin(), (x).end()
#define rrng(x) (x).rbegin(), (x).rend()
#define sz(x) ((int)(x).size())
#define pb push_back
#define fi first
#define se second
#define pcnt __builtin_popcountll

using namespace std;
using namespace atcoder;

using ll = long long;
using ld = long double;
template<typename T> using mpq = priority_queue<T, vector<T>, greater<T>>;
template<typename T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<typename T> bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
template<typename T> ll sumv(const vector<T>&a){ll res(0);for(auto&&x:a)res+=x;return res;}
bool yn(bool a) { if(a) {cout << "Yes" << endl; return true;} else {cout << "No" << endl; return false;}}
#define retval(x) {cout << #x << endl; return;}
#define cout2(x,y) cout << x << " " << y << endl;
#define coutp(p) cout << p.fi << " " << p.se << endl;
#define out cout << ans << endl;
#define outd cout << fixed << setprecision(20) << ans << endl;
#define outm cout << ans.val() << endl;
#define outv fore(yans , ans) cout << yans << "\n";
#define outdv fore(yans , ans) cout << yans.val() << "\n";
#define assertmle(x) if (!(x)) {vi v(3e8);}
#define asserttle(x) if (!(x)) {while(1){}}
#define coutv(v) {fore(vy , v) {cout << vy << " ";} cout << endl;}
#define coutv2(v) fore(vy , v) cout << vy << "\n";
#define coutvm(v) {fore(vy , v) {cout << vy.val() << " ";} cout << endl;}
#define coutvm2(v) fore(vy , v) cout << vy.val() << "\n";
using pll = pair<ll,ll>;using pil = pair<int,ll>;using pli = pair<ll,int>;using pii = pair<int,int>;using pdd = pair<ld,ld>;
using vi = vector<int>;using vd = vector<ld>;using vl = vector<ll>;using vs = vector<string>;using vb = vector<bool>;
using vpii = vector<pii>;using vpli = vector<pli>;using vpll = vector<pll>;using vpil = vector<pil>;
using vvi = vector<vector<int>>;using vvl = vector<vector<ll>>;using vvs = vector<vector<string>>;using vvb = vector<vector<bool>>;
using vvpii = vector<vector<pii>>;using vvpli = vector<vector<pli>>;using vvpll = vector<vpll>;using vvpil = vector<vpil>;
using mint = modint998244353;
//using mint = modint1000000007;
//using mint = dynamic_modint<0>;
using vm = vector<mint>;
using vvm = vector<vector<mint>>;
vector<int> dx={1,0,-1,0,1,1,-1,-1},dy={0,1,0,-1,1,-1,1,-1};
ll gcd(ll a, ll b) { return a?gcd(b%a,a):b;}
ll lcm(ll a, ll b) { return a/gcd(a,b)*b;}
#define yes {cout <<"Yes"<<endl;}
#define no {cout <<"No"<<endl;}
const double eps = 1e-10;
const ll LINF = 1001002003004005006ll;
const int INF = 1001001001;
#ifdef MY_LOCAL_DEBUG
#include "./debug/localDebug.cpp"
#define showp(p) cerr<<#p<<" = "<<p.fi<<" : "<<p.se<<endl
#define show1(a) cerr<<#a<<" = "<<a<<endl
#define show2(a,b) cerr<<#a<<" = "<<a<<" : "<<#b<<" = "<<b<<endl
#define show3(a,b,c) cerr<<#a<<" = "<<a<<" : "<<#b<<" = "<<b<<" : "<<#c<<" = "<<c<<endl
#define show4(a,b,c,d) cerr<<#a<<" = "<<a<<" : "<<#b<<" = "<<b<<" : "<<#c<<" = "<<c<<" : "<<#d<<" = "<<d<<endl
#define show5(a,b,c,d,e) cerr<<#a<<" = "<<a<<" : "<<#b<<" = "<<b<<" : "<<#c<<" = "<<c<<" : "<<#d<<" = "<<d<<" : "<<#e<<" = "<<e<<endl
#define DEBUG_LINE cout << "DEBUG_LINE : " << __LINE__ << endl
#define showv(v) {cout<<#v<<" : "; fore(vy , v) {cout << vy << " ";} cout << endl;}
#define showv2(v) {cout<<#v<<endl; fore(vy , v) cout << vy << "\n";}
#define showvm(v) {cout<<#v<<" : "; fore(vy , v) {cout << vy.val() << " ";} cout << endl;}
#define showvm2(v) {cout<<#v<<endl; fore(vy , v) cout << vy.val() << "\n";}
#define showmat(v) {cout<<#v<<endl; fore(row , v) { fore(seg , row) cout << seg << " "; cout << endl;}}
#define showmatm(v) {cout<<#v<<endl; fore(row , v) { fore(seg , row) cout << seg.val() << " "; cout << endl;}}
#else
#define showp(p)
#define show1(a)
#define show2(a,b)
#define show3(a,b,c)
#define show4(a,b,c,d)
#define show5(a,b,c,d,e)
#define DEBUG_LINE
#define showv(v)
#define showv2(v)
#define showvm(v)
#define showvm2(v)
#define showmat(v)
#define showmatm(v)
#endif
#define overload5(a,b,c,d,e,f, ...) f
#define show(...) overload5(__VA_ARGS__, show5, show4, show3, show2, show1)(__VA_ARGS__)

struct base{
    multiset<ll> top;
    ll top_sum;
    multiset<ll> down;
    ll down_sum;
    ll ans;

    base(){
    }

    void _push_top(ll a){
        top.insert(a);
        top_sum += a;
    }
    void _push_down(ll a){
        down.insert(a);
        down_sum += a;
    }
    ll _pop_top(){
        ll ret = *(top.begin());
        top_sum -= ret;
        top.erase(top.begin());
        return ret;
    }
    ll _pop_down(){
        auto it = down.end();
        it--;
        ll ret = *(it);
        down_sum -= ret;
        down.erase(it);
        return ret;
    }
    void _erase_top(ll a){
        auto it = top.lower_bound(a);
        assert(*it==a);
        top_sum -= *it;
        top.erase(it);
    }
    void _erase_down(ll a){
        auto it = down.lower_bound(a);
        assert(*it==a);
        down_sum -= *it;
        down.erase(it);
    }
    void _add(ll a){
        if (sz(top)==0 || *(top.begin()) <= a){
            _push_top(a);
        }else{
            _push_down(a);
        }
        if (sz(top) < sz(down)){
            ll a = _pop_down();
            _push_top(a);
        }
        if (sz(top) > sz(down)+1){
            ll a = _pop_top();
            _push_down(a);
        }
        ll l = *(top.begin());
        ans = (top_sum - l*sz(top)) + (l*sz(down) - down_sum);
    }
    void _del(ll a){
        if (sz(top)==0 || *(top.begin()) <= a){
            _erase_top(a);
        }else{
            _erase_down(a);
        }
        if (sz(top) < sz(down)){
            ll a = _pop_down();
            _push_top(a);
        }
        if (sz(top) > sz(down)+1){
            ll a = _pop_top();
            _push_down(a);
        }
        if (sz(top)){
            ll l = *(top.begin());
            ans = (top_sum - l*sz(top)) + (l*sz(down) - down_sum);
        }else{
            ans = 0;
        }
    }
};

struct upper : base{
    ll mx;

    upper(ll a) : mx(a){
        ans = 0;
        top_sum = 0;
        down_sum = 0;
    }

    void add(ll a){
        if (mx < a) swap(mx,a);
        _add(a);
    }

    void erase(ll a){
        if (mx == a){
            auto it = top.end();
            it--;
            a = *it;
            mx = a;
        }
        _del(a);
    }

    ll get(){
        ll mn = mx;
        if (sz(top)){
            chmin(mn, *(top.begin()));
        }
        if (sz(down)){
            chmin(mn, *(down.begin()));
        }
        if (mn==mx) return 1;
        return ans;
    }
};

struct lower : upper{

    lower(ll a) : upper(-a){
    }

    void add2(ll a){
        add(-a);
    }

    void erase2(ll a){
        erase(-a);
    }
};

void solve(){
    int n; cin>>n;
    vl a(n+1);
    rep(i,n+1) cin>>a[i];
    vvi e(n+1);
    rep(i,n){
        int c,d; cin>>c>>d;
        e[c].pb(d);
        e[d].pb(c);
    }
    upper nu(a[0]);
    lower nl(a[0]);
    vl ans(n+1);

    int now = 0;

    auto dfs = [&](auto dfs,int x,int pre)->void{
        if (x!=0){
            nu.add(a[x]);
            nl.add2(a[x]);
        }
        now++;
        if (now>2){
            ans[x] = min(nu.get() , nl.get());
        }else ans[x] = -1;
        fore(y , e[x]){
            if(y == pre) continue;
            dfs(dfs, y, x);
        }
        if (x!=0){
            nu.erase(a[x]);
            nl.erase2(a[x]);
        }
        now--;
        return;
    };
    dfs(dfs,0,-1);

    rep1(i,n+1) cout << ans[i] << endl;

    return;
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);

    int t = 1;
    //cin>>t;

    rep(i,t){
        solve();
    }

    return 0;
}