#line 1 "main.cpp"
//#pragma GCC target("avx,avx2")
//#pragma GCC optimize("O3")
//#pragma GCC optimize("unroll-loops")
#include<bits/stdc++.h>
#ifdef LOCAL
#include <debug.hpp>
#define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#define debug(...) (static_cast<void>(0))
#endif
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll, ll>;
using pii = pair<int, int>;
using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vul = vector<ull>;
using vpii = vector<pii>;
using vpll = vector<pll>;
using vs = vector<string>;
template<class T> using pq = priority_queue<T, vector<T>, greater<T>>;
#define overload4(_1, _2, _3, _4, name, ...) name
#define overload3(a,b,c,name,...) name
#define rep1(n) for (ll UNUSED_NUMBER = 0; UNUSED_NUMBER < (n); ++UNUSED_NUMBER)
#define rep2(i, n) for (ll i = 0; i < (n); ++i)
#define rep3(i, a, b) for (ll i = (a); i < (b); ++i)
#define rep4(i, a, b, c) for (ll i = (a); i < (b); i += (c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep1(n) for(ll i = (n) - 1;i >= 0;i--)
#define rrep2(i,n) for(ll i = (n) - 1;i >= 0;i--)
#define rrep3(i,a,b) for(ll i = (b) - 1;i >= (a);i--)
#define rrep4(i,a,b,c) for(ll i = (a) + ((b)-(a)-1) / (c) * (c);i >= (a);i -= c)
#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define all1(i) begin(i) , end(i)
#define all2(i,a) begin(i) , begin(i) + a
#define all3(i,a,b) begin(i) + a , begin(i) + b
#define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__)
#define sum(...) accumulate(all(__VA_ARGS__),0LL)
template<class T> bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } else return 0; }
template<class T> bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } else return 0; }
template<class T> auto min(const T& a){return *min_element(all(a));}
template<class T> auto max(const T& a){return *max_element(all(a));}
template<class... Ts> void in(Ts&... t);
#define INT(...) int __VA_ARGS__; in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__; in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__; in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__; in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__; in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__; in(__VA_ARGS__)
#define VEC(type, name, size) vector<type> name(size); in(name)
#define VV(type, name, h, w) vector<vector<type>> name(h, vector<type>(w)); in(name)
ll intpow(ll a, ll b){ ll ans = 1; while(b){if(b & 1) ans *= a; a *= a; b /= 2;} return ans;}
ll modpow(ll a, ll b, ll p){ ll ans = 1; a %= p;if(a < 0) a += p;while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; }
void Yes() {cout << "Yes\n";return;}
void No() {cout << "No\n";return;}
void YES() {cout << "YES\n";return;}
void NO() {cout << "NO\n";return;}
void First() {cout << "First\n";return;}
void Second() {cout << "Second\n";return;}
namespace IO{
#define VOID(a) decltype(void(a))
struct setting{ setting(){cin.tie(nullptr); ios::sync_with_stdio(false);fixed(cout); cout.precision(12);}} setting;
template<int I> struct P : P<I-1>{};
template<> struct P<0>{};
template<class T> void i(T& t){ i(t, P<3>{}); }
void i(vector<bool>::reference t, P<3>){ int a; i(a); t = a; }
template<class T> auto i(T& t, P<2>) -> VOID(cin >> t){ cin >> t; }
template<class T> auto i(T& t, P<1>) -> VOID(begin(t)){ for(auto&& x : t) i(x); }
template<class T, size_t... idx> void ituple(T& t, index_sequence<idx...>){in(get<idx>(t)...);}
template<class T> auto i(T& t, P<0>) -> VOID(tuple_size<T>{}){ituple(t, make_index_sequence<tuple_size<T>::value>{});} 
#undef VOID
}
#define unpack(a) (void)initializer_list<int>{(a, 0)...}
template<class... Ts> void in(Ts&... t){ unpack(IO :: i(t)); }

#undef unpack
static const double PI = 3.1415926535897932;
template <class F> struct REC {
    F f;
    REC(F &&f_) : f(forward<F>(f_)) {}
    template <class... Args> auto operator()(Args &&...args) const { return f(*this, forward<Args>(args)...); }};

constexpr int mod = 998244353;
//constexpr int mod = 1000000007;
#line 2 "library/segtree/segtree.hpp"
template <typename T, typename OP>
struct segtree {
    int N;
    int size;
    vector<T> seg;
    const OP op;
    const T I;
    segtree(OP _op, const T &I_) : N(0), size(0), op(_op), I(I_) {}
    segtree(int _N, OP _op, const T &I_) : op(_op), I(I_) { init(_N); }
    segtree(const vector<T> &v, OP _op, T I_) : op(_op), I(I_) {
        init(v.size());
        for (int i = 0; i < (int)v.size(); i++) {
            seg[i + size] = v[i];
        }
        build();
    }
    void init(int _N) {
        N = _N;
        size = 1;
        while (size < N) size <<= 1;
        seg.assign(2 * size, I);
    }
    void build() {
        for (int k = size - 1; k > 0; k--) {
            seg[k] = op(seg[2 * k], seg[2 * k + 1]);
        }
    }
    void set(int p, T x) {
        assert(0 <= p && p < N);
        p += size;
        seg[p] = x;
        while (p >>= 1) {
            seg[p] = op(seg[2 * p], seg[2 * p + 1]);
        }
    }
    void add(int p, T x) {
        assert(0 <= p && p < N);
        p += size;
        seg[p] += x;
        while (p >>= 1) {
            seg[p] = op(seg[2 * p], seg[2 * p + 1]);
        }
    }
    T get(int p) const {
        assert(0 <= p && p < N);
        return seg[p + size];
    }
    // query to [l, r)
    T prod(int l, int r) {
        assert(0 <= l && l <= r && r <= N);
        T L = I, R = I;
        for (l += size, r += size; l < r; l >>= 1, r >>= 1) {
            if (l & 1) L = op(L, seg[l++]);
            if (r & 1) R = op(seg[--r], R);
        }
        return op(L, R);
    }
    T all_prod() {return seg[1];}
    // check(a[l] * ...  * a[r-1]) が true となる最大の r
    // (右端まですべて true なら N を返す)
    template <class C>
    int max_right(int l, C check) {
        assert(0 <= l && l <= N);
        assert(check(I) == true);
        if (l == N) return N;
        l += size;
        T sm = I;
        do {
            while (l % 2 == 0) l >>= 1;
            if (!check(op(sm, seg[l]))) {
                while (l < size) {
                    l = (2 * l);
                    if (check(op(sm, seg[l]))) {
                        sm = op(sm, seg[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, seg[l]);
            l++;
        } while ((l & -l) != l);
        return N;
    }
    // check(a[l] * ... * a[r-1]) が true となる最小の l
    // (左端まで true なら 0 を返す)
    template <typename C>
    int min_left(int r, C check) {
        assert(0 <= r && r <= N);
        assert(check(I) == true);
        if (r == 0) return 0;
        r += size;
        T sm = I;
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!check(op(seg[r], sm))) {
                while (r < size) {
                    r = (2 * r + 1);
                    if (check(op(seg[r], sm))) {
                        sm = op(seg[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(seg[r], sm);
        } while ((r & -r) != r);
        return 0;
    }
};
#line 92 "main.cpp"
using T = ll;
T op(T x,T y) {return x + y;}
T e() {return 0;}
void solve() {
    INT(n);
    VEC(int,a,n+1);
    vvi g(n+1);
    rep(i,n) {
        INT(u,v);
        g[u].emplace_back(v);
        g[v].emplace_back(u);
    }
    vi A = a;
    sort(all(A));
    A.erase(unique(all(A)),A.end());
    vi ans(n+1,-1);
    segtree<ll,decltype(&op)> seg1(A.size(),op,e()),seg2(A.size(),op,e());
    auto ff = [](ll u) {
        return u == 0;
    };
    ll thr = 0;
    auto h = [&](ll u) {
        return u < thr;
    };
    auto dfs = REC([&](auto &&f,int now,int par) -> void {
        int id = lower_bound(all(A),a[now]) - A.begin();
        seg1.add(id,1);
        seg2.add(id,a[now]);
        if(seg1.all_prod() >= 3) {
            int si = seg1.all_prod() - 1;
            ll tmp = 4e18;
            int miid = seg1.max_right(0,ff);
            int maid = seg2.min_left(A.size(),ff);
            if(miid == maid - 1) {
                tmp = 1;
            }
            else {
                thr = si / 2 + 1;
                int R = seg1.max_right(0,h);
                thr++;
                int R2 = seg1.max_right(0,h);
                ll tmp1 = A[R2] * (seg1.prod(0,R2) - 1) - seg2.prod(0,R2) + A[miid];
                tmp1 += seg2.prod(R2,A.size()) - A[R2] * seg1.prod(R2,A.size());
                debug(now,R2,A[R2],seg1.prod(0,R2),seg2.prod(0,R2),seg2.prod(R2,A.size()),seg1.prod(R2,A.size()));
                thr = si / 2;
                R = seg1.max_right(0,h);
                thr++;
                R2 = seg1.max_right(0,h);
                ll tmp2 = A[R2] * seg1.prod(0,R2) - seg2.prod(0,R2);
                tmp2 += seg2.prod(R2,A.size()) - A[maid-1] - A[R2] * (seg1.prod(R2,A.size()) - 1);
                tmp = min(tmp1,tmp2);
                //debug(now,seg1.prod(0,R),seg1.prod(R,A.size()),seg2.prod(0,R),seg2.prod(R,A.size()));
                debug(now,tmp1,tmp2,R,R2,miid,maid-1);
            }
            ans[now] = tmp;
        }
        for(auto &nex:g[now]) {
            if(nex != par) {
                f(nex,now);
            }
        }
        seg1.add(id,-1);
        seg2.add(id,-a[now]);
    });
    dfs(0,-1);
    rep(i,1,n+1) cout << ans[i] << '\n';
}

int main() {
	//INT(TT);	
    int TT = 1;
	while(TT--) solve();
}