1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
//~ while (clock()<=69*CLOCKS_PER_SEC)
//~ #pragma comment(linker, "/stack:200000000")
#pragma GCC optimize("O3")
//~ #pragma GCC optimize("Ofast")
//~ #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
//~ #pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>

using namespace std;

using ll=long long;
using ld=long double;
using pii=pair<int, int>;
using pll=pair<ll, ll>;
using vi=vector<int>;
using vll=vector<ll>;

template<class TH> void _dbg(const char *sdbg, TH h){ cerr<<sdbg<<" = "<<h<<endl; }
#ifdef LOCAL
#define _upgrade ios_base::sync_with_stdio(0);
#define debug(...) _dbg(#__VA_ARGS__, __VA_ARGS__);
#else
#define _upgrade ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
#define debug(...) 98;
#define cerr if(0) cout
#endif

#define pb push_back
#define mp make_pair
#define all(x) x.begin(),x.end()
#define sz(x) ((int)(x).size())
#define fi first
#define se second

#define erase_duplicates(x) sort(all(x)), (x).resize(distance((x).begin(), unique(all(x))));

#define watch(x) cout << (#x) << " is " << (x) << endl;

#define pow2(x) ((x)*(x))
#define mod(x, m) ((((x) % (m)) + (m)) % (m))
#define max3(a, b, c) max(a, max(b, c))
#define min3(a, b, c) min(a, min(b, c))

#define REP(i, a, b) for(int i = a; i <= b; ++i)
#define REPV(i, b, a) for(int i = b; i >= a; --i)

#define mytype pair<ll,pair<ll, int> >

const double m_pi = acos(-1.0);
const int int_max = 0x3f3f3f3f;
const int M7 = 1000*1000*1000+7;
const int M9 = 1000*1000*1000+9;

ll power[100'000];
// vector<mytype> downResults[100'000];
ll lastCount = -1;

vector<pair<int, ll> > tos[100'000];

vector<mytype> dfsBasic (int pos, int father) {

    vector<mytype> ret;
    vector<vector<mytype> > results;
    vector<ll> dists;

    REP(i,0,sz(tos[pos])-1) {
        int v = tos[pos][i].fi;
        if(v == father) continue;
        ll dist = tos[pos][i].se;
        auto result = dfsBasic(v, pos);
        results.pb(result);
        dists.pb(dist);
    }
    REP(i,0,sz(results)-1) {
        REP(j, 0, sz(results[i])-1) {
            results[i][j].fi += dists[i];
        }
        ret.insert( ret.end(), results[i].begin(), results[i].end());
    }

    ret.push_back(mp(
        0LL,
        mp(
            power[pos],
            1
        )
    ));
    sort(ret.begin(), ret.end());

    vector<mytype> retFixed;
    REP(i,0,sz(ret)-1) {
        auto curr = ret[i];
        while(i+1 < sz(ret)) {
            if(curr.se.fi < ret[i+1].fi)break;
            curr.se.se += ret[i+1].se.se;
            curr.se.fi = max(curr.se.fi, ret[i+1].se.fi - ret[i+1].fi);
            ++i;
        }
        retFixed.pb(curr);
    }
    

    lastCount = retFixed[0].se.se;

    return retFixed;
}

int main() {
    _upgrade
    mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
    cout<<fixed<<setprecision(15);

    int n;cin>>n;
    REP(i, 0, n-1) {
        cin>>power[i];
    }
    REP(i,0,n-2) {
        int a, b;ll c;
        cin>>a>>b>>c;--a;--b;
        tos[a].pb(mp(b,c));
        tos[b].pb(mp(a,c));
    }

    REP(i, 0, n-1) {
        dfsBasic(i, i);
        cout<<lastCount<<" ";
    }



    return 0;
}




/*
    __builtin_popcount count total set bits on a given integer
    (use __builtin_popcountll for long long).


*/