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#include <bits/stdc++.h>
#define MP make_pair
#define PB push_back
#define int long long
#define st first
#define nd second
#define rd third
#define FOR(i, a, b) for(int i =(a); i <=(b); ++i)
#define RE(i, n) FOR(i, 1, n)
#define FORD(i, a, b) for(int i = (a); i >= (b); --i)
#define REP(i, n) for(int i = 0;i <(n); ++i)
#define VAR(v, i) __typeof(i) v=(i)
#define FORE(i, c) for(VAR(i, (c).begin()); i != (c).end(); ++i)
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((int)(x).size())
#define __builtin_ctz __builtin_ctzll
#define __builtin_clz __builtin_clzll
#define __builtin_popcount __builtin_popcountll
using namespace std;
template<typename TH> void _dbg(const char* sdbg, TH h) { cerr<<sdbg<<"="<<h<<"\n"; }
template<typename TH, typename... TA> void _dbg(const char* sdbg, TH h, TA... t) {
  while(*sdbg != ',') { cerr<<*sdbg++; } cerr<<"="<<h<<","; _dbg(sdbg+1, t...);
}
#ifdef LOCAL
#define debug(...) _dbg(#__VA_ARGS__, __VA_ARGS__)
#define debugv(x) {{cerr <<#x <<" = "; FORE(itt, (x)) cerr <<*itt <<", "; cerr <<"\n"; }}
#else
#define debug(...) (__VA_ARGS__)
#define debugv(x)
#define cerr if(0)cout
#endif
#define next ____next
#define prev ____prev
#define left ____left
#define hash ____hash
typedef long long ll;
typedef long double LD;
typedef pair<int, int> PII;
typedef pair<ll, ll> PLL;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<ll> VLL;
typedef vector<pair<int, int> > VPII;
typedef vector<pair<ll, ll> > VPLL;

template<class C> void mini(C&a4, C b4){a4=min(a4, b4); }
template<class C> void maxi(C&a4, C b4){a4=max(a4, b4); }
template<class T1, class T2>
ostream& operator<< (ostream &out, pair<T1, T2> pair) { return out << "(" << pair.first << ", " << pair.second << ")";}
template<class A, class B, class C> struct Triple { A first; B second; C third;
  bool operator<(const Triple& t) const { if (st != t.st) return st < t.st; if (nd != t.nd) return nd < t.nd; return rd < t.rd; } };
template<class T> void ResizeVec(T&, vector<int>) {}
template<class T> void ResizeVec(vector<T>& vec, vector<int> sz) {
  vec.resize(sz[0]); sz.erase(sz.begin()); if (sz.empty()) { return; }
  for (T& v : vec) { ResizeVec(v, sz); }
}
typedef Triple<int, int, int> TIII;
template<class A, class B, class C>
ostream& operator<< (ostream &out, Triple<A, B, C> t) { return out << "(" << t.st << ", " << t.nd << ", " << t.rd << ")"; }
template<class T> ostream& operator<<(ostream& out, vector<T> vec) { out<<"("; for (auto& v: vec) out<<v<<", "; return out<<")"; }
template<class T> ostream& operator<<(ostream& out, set<T> vec) { out<<"("; for (auto& v: vec) out<<v<<", "; return out<<")"; }
template<class L, class R> ostream& operator<<(ostream& out, map<L, R> vec) { out<<"("; for (auto& v: vec) out<<v<<", "; return out<<")"; }

const int N = 1e5 + 5;
vector<pair<int32_t, int>> slo[N];
int r[N];

void DelEdge(int v, int nei) {
  for (int i = 0; i < SZ(slo[v]); i++) {
    if (slo[v][i].st == nei) {
      swap(slo[v][i], slo[v].back());
      slo[v].pop_back();
      return;
    }
  }
}

int32_t sz[N];
int dis[N];


struct Ev {
  int32_t v;
  int dis;
  bool to;
  bool operator<(const Ev& oth) const {
    if (dis != oth.dis) { return dis < oth.dis; }
    return to > oth.to;
  }
  friend ostream& operator<<(ostream& out, Ev e) {
    return out<<"("<<e.v<<", "<<e.dis<<", "<<e.to<<")";
  }
};

vector<Ev> evs;
bool gather;
int32_t CntSzCent(int32_t v, int32_t size, int32_t par) {
  sz[v] = 1;
  if (gather) {
    evs.PB({v, dis[v], 1});
    if (r[v] >= dis[v]) {
      evs.PB({v, r[v] - dis[v], 0});
    }
  }
  int ret = 0;
  for (int i = 0; i < SZ(slo[v]); i++) {
    int nei = slo[v][i].st;
    if (par == nei) { continue; }
    dis[nei] = dis[v] + slo[v][i].nd;
    int cnt_rec = CntSzCent(nei, size, v);
    sz[v] += sz[nei];
    if (cnt_rec) {
      ret = cnt_rec;
    }
  }
  if (ret == 0) {
    if (sz[v] >= size / 2) {
      return v;
    } else {
      return 0;
    }
  } else {
    return ret;
  }
}

vector<vector<int32_t>> d;

void Rec(int32_t v, int32_t size) {
  gather = false;
  v = CntSzCent(v, size, -1);
  dis[v] = 0;
  gather = true;
  evs.clear();
  CntSzCent(v, size, -1);
  sort(ALL(evs));
//   debug(v);
//   debug(evs);
  //int st = SZ(d);
  assert(!evs.empty() && evs[0].to == 1);
  d.PB({});
  REP (i, SZ(evs)) {
    if (evs[i].to == 1 && i && evs[i - 1].to == 0) {
      d.PB({evs[i].v, (int32_t)SZ(d) - 1});
    } else if (evs[i].to) {
      d.back().PB(evs[i].v);
    } else {
      d[evs[i].v].PB(SZ(d) - 1);
    }
  }
  if (evs.back().to == 1) {
    d.pop_back();
  }
  for (int i = 0; i < SZ(slo[v]); i++) {
    int nei = slo[v][i].st;
    DelEdge(nei, v);
    Rec(nei, sz[nei]);
  }
}
int n;
// VI vis;
// int reach;

// void Dfs(int v) {
//   vis[v] = 1;
//   if (v <= n) { reach++; }
//   for (auto nei : d[v]) {
//     if (vis[nei]) { continue; }
//     Dfs(nei);
//   }
// }
VVI trans;
const int C = 1000;
typedef bitset<C> B;
LD Timestamp() {
  return 1. * clock() / CLOCKS_PER_SEC;
}
int32_t main() {

  ios_base::sync_with_stdio(0);
  cout << fixed << setprecision(10);
  cerr << fixed << setprecision(10);
  cin.tie(0);
  //double beg_clock = 1.0 * clock() / CLOCKS_PER_SEC;
  
  cin>>n;
  RE (i, n) {
    cin>>r[i];
  }
  d.resize(n + 1);
  RE (i, n - 1) {
    int a, b, c;
    cin>>a>>b>>c;
    slo[a].PB({b, c});
    slo[b].PB({a, c});
  }
  
  Rec(1, n);
  
  //debug(Timestamp());
  
  int D = SZ(d);
  trans.resize(D);
  RE (i, D - 1) {
    for (auto v : d[i]) {
      trans[v].PB(i);
    }
  }
  
  
  vector<int32_t> ktop(D);
  vector<int32_t> vis(D);
  int post = 0;
  function<void(int)> Dfs1 = [&](int w) {
    vis[w] = 1;
    for (auto nei : d[w]) {
      if (vis[nei]) { continue; }
      Dfs1(nei);
    }
    post++;
    ktop[post] = w;
  };
  
  int H = 0;
  RE (i, D - 1) {
    H += SZ(d[i]);
    if (vis[i] == 0) {
      Dfs1(i);
    }
  }
  
  int cnt_ss = 0;
  vector<int32_t> ss(D);
  vector<vector<int32_t>> by_ss(1);
  function<void(int)> Dfs2 = [&](int v) {
    ss[v] = cnt_ss;
    by_ss[cnt_ss].PB(v);
    for (auto nei : trans[v]) {
      if (ss[nei] == 0) {
        Dfs2(nei);
      }
    }
  };
  
  FORD (i, D - 1, 1) {
    int v = ktop[i];
    if (ss[v] == 0) {
      cnt_ss++;
      by_ss.PB({});
      Dfs2(v);
    }
  }
  
  vector<vector<int32_t>> nowy(cnt_ss + 1);
  vector<int32_t> last(cnt_ss + 1);
  int E = 0;
  RE (ss_ind, cnt_ss) {
    for (auto v : by_ss[ss_ind]) {
      assert(ss[v] == ss_ind);
      for (auto nei : d[v]) {
        if (ss[nei] != ss_ind && last[ss[nei]] != ss_ind) {
          assert(ss_ind <= ss[nei]);
          last[ss[nei]] = ss_ind;
          nowy[ss_ind].PB(ss[nei]);
          E++;
        }
      }
    }
  }
  debug(D, H, cnt_ss, E);
  
  int st = 1;
  vector<B> reaches(cnt_ss + 1);
  vector<int32_t> ans(cnt_ss + 1);
  vector<bool> any(cnt_ss + 1);
  VI ord{0};
  RE (i, D - 1) {
    if (ktop[i] <= n) {
      ord.PB(ktop[i]);
    }
  }
  assert(SZ(ord) == n + 1);
  //debug(ord);
  while (st <= n) {
    RE (ss_ind, cnt_ss) {
      if (any[ss_ind]) {
        reaches[ss_ind].reset();
        any[ss_ind] = 0;
      }
    }
    FOR (i, st, min(st + C - 1, n)) {
      int v = ord[i];
      reaches[ss[v]][i - st] = 1;
      any[ss[v]] = 1;
    }
    FORD (ss_ind, cnt_ss, 1) {
      for (auto nei : nowy[ss_ind]) {
        if (any[nei]) {
          reaches[ss_ind] |= reaches[nei];
          any[ss_ind] = 1;
        }
      }
      if (any[ss_ind]) {
        ans[ss_ind] += reaches[ss_ind].count();
      }
    }
    st += C;
  }
  RE (i, n) {
    cout<<ans[ss[i]]<<" ";
  }
  cout<<endl;
    
  
  
  
//   RE (i, n) {
//     reach = 0;
//     REP (j, SZ(d)) {
//       vis[j] = 0;
//     }
//     Dfs(i);
//     cout<<reach<<" ";
//   }
//   cout<<endl;
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  return 0;
}