#include<bits/stdc++.h>
using namespace std;
#define ll long long
const int maxn=200005;
const ll inf=1e18;
vector<int> s[maxn+5],nd[maxn+5],rn[maxn+5];
vector<int> an;
int dg[maxn+5],pt[maxn+5],vis[maxn+5],ps[maxn+5],vt;
ll f[maxn+5],g[maxn+5];
int n;
bool cmp(int a,int b){return dg[a]<dg[b];}
void dfs(int u,int p,int q){
    vis[u]=vt;
    while(pt[u]<s[u].size()&&dg[s[u][pt[u]]]<q)pt[u]++;
    int ni=pt[u];
    vector<ll> cs;
    ll bs=0,sc=0;
    for(int i=pt[u];i<s[u].size();i++){
        int v=s[u][i];
        if(v==p)continue;
        dfs(v,u,q);
        bs+=f[v];
        if(g[v]!=-inf)cs.push_back(max(0LL,g[v]-f[v]));
        else cs.push_back(0);
    }
    sort(cs.begin(),cs.end());
    for(auto c:cs)sc+=c;
    ll vnc=bs+sc;
    ll vc=-inf;
    if(ni+(int)cs.size()>=q){
        int ndd=max(0,q-ni);
        ll cur=0;
        for(int i=0;i<ndd;i++)cur+=cs[i];
        vc=1+bs+sc-cur;
    }
    f[u]=max(vnc,vc);
    g[u]=-inf;
    if(q>0&&ni+(int)cs.size()>=q-1){
        int ndd=max(0,q-1-ni);
        ll cur=0;
        for(int i=0;i<ndd;i++)cur+=cs[i];
        g[u]=1+bs+sc-cur;
    }
}
int main(){
    int i,j,k,c,u,v,e;
    scanf("%d",&n);
    for(i=1;i<=n;i++){
        scanf("%d",&c);
        dg[i]=c;
        nd[c].push_back(i);
        for(j=0;j<c;j++){
            scanf("%d",&e);
            rn[e].push_back(i);
        }
    }
    for(i=1;i<n;i++){
        u=rn[i][0];v=rn[i][1];
        s[u].push_back(v);
        s[v].push_back(u);
    }
    for(i=1;i<=n;i++){
        sort(s[i].begin(),s[i].end(),cmp);
        an.push_back(i);
        ps[i]=i-1;
    }
    for(i=1;i<n;i++){
        vt++;
        ll ans=0;
        for(auto u:nd[i-1]){
            int idx=ps[u];
            int last=an.back();
            an[idx]=last;
            ps[last]=idx;
            an.pop_back();
        }
        for(auto u:an){
            while(pt[u]<s[u].size()&&dg[s[u][pt[u]]]<i)pt[u]++;
            if(vis[u]!=vt){
                dfs(u,0,i);
                ans+=f[u];
            }
        }
        printf("%lld%c",ans,i==n-1?'\n':' ');
    }
    return 0;
}