Problem:
Score : 2200 points

Problem Statement

You are given N-1 subsets of \{1,2,...,N\}. Let the i-th set be E_i.

Let us choose two distinct elements u_i and v_i from each set E_i, and consider a graph T with N vertices and N-1 edges, whose vertex set is \{1,2,..,N\} and whose edge set is (u_1,v_1),(u_2,v_2),...,(u_{N-1},v_{N-1}).
Determine if T can be a tree by properly deciding u_i and v_i.
If it can, additionally find one instance of (u_1,v_1),(u_2,v_2),...,(u_{N-1},v_{N-1}) such that T is actually a tree.

Constraints

2 \leq N \leq 10^5

E_i is a subset of \{1,2,..,N\}.

|E_i| \geq 2

The sum of |E_i| is at most 2 \times 10^5.

Input

Input is given from Standard Input in the following format:

N
c_1 w_{1,1} w_{1,2} ... w_{1,c_1}
:
c_{N-1} w_{N-1,1} w_{N-1,2} ... w_{N-1,c_{N-1}}

Here, c_i stands for the number of elements in E_i, and w_{i,1},...,w_{i,c_i} are the c_i elements in c_i.
Here, 2 \leq c_i \leq N, 1 \leq w_{i,j} \leq N, and w_{i,j} \neq w_{i,k} (1 \leq j < k \leq c_i) hold.

Output

If T cannot be a tree, print -1; otherwise, print the choices of (u_i,v_i) that satisfy the condition, in the following format:

u_1 v_1
:
u_{N-1} v_{N-1}

Sample Input 1

5
2 1 2
3 1 2 3
3 3 4 5
2 4 5

Sample Output 1

1 2
1 3
3 4
4 5

Sample Input 2

6
3 1 2 3
3 2 3 4
3 1 3 4
3 1 2 4
3 4 5 6

Sample Output 2

-1

Sample Input 3

10
5 1 2 3 4 5
5 2 3 4 5 6
5 3 4 5 6 7
5 4 5 6 7 8
5 5 6 7 8 9
5 6 7 8 9 10
5 7 8 9 10 1
5 8 9 10 1 2
5 9 10 1 2 3

Sample Output 3

1 2
2 3
3 4
4 5
5 6
6 7
7 8
8 9
9 10

Solution in C++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include<bits/stdc++.h>
#define maxn 200050
#define maxm 400050
using namespace std;
typedef long long LL;

int n;
int vs,vt;

vector<int> G[maxn];

int tot;
int cost[maxm<<1];
int head[maxn],edge[maxm<<1],nxt[maxm<<1];

void join(int u,int v)
{
    // cout<<"edge:"<<u<<" "<<v<<endl;
    cost[tot]=1; edge[tot]=v; nxt[tot]=head[u]; head[u]=tot++;
    cost[tot]=0; edge[tot]=u; nxt[tot]=head[v]; head[v]=tot++;
}

void init()
{
    tot=0;
    memset(head,-1,sizeof(head));

    scanf("%d",&n);
    vs=n+n,vt=n+n+1;
    for (int k=1;k<n;++k)
    {
        int x,v;
        scanf("%d",&x);
        while (x--)
        {
            scanf("%d",&v);
            G[v].push_back(k);
            join(v,k+n);
        }
    }
    for (int i=1;i<=n;++i)  join(vs,i);
    for (int i=n+1;i<n+n;++i)   join(i,vt);
}

int d[maxn],gap[maxn];
int cur[maxn],prt[maxn];

int isap()
{
    for (int i=1;i<=vt;++i) cur[i]=head[i],++gap[d[i]=0];
    int i=vs,ans=0;
    while (d[vs]<vt)
    {
        if (i==vt)
        {
            for (++ans;i!=vs;i=edge[prt[i]^1])
                // cout<<"path:"<<i<<endl,
                --cost[prt[i]],++cost[prt[i]^1];
            // cout<<"path:"<<vs<<endl<<endl;
        }

        bool flag=0;
        for (int k=cur[i];~k;k=nxt[k])
        {
            int j=edge[k];
            if (cost[k]&&d[i]==d[j]+1)
            {
                flag=1;
                cur[i]=prt[j]=k;
                i=j;
                break;
            }
        }

        if (flag)   continue;

        if (--gap[d[i]]==0) break;
        d[i]=vt;
        for (int k=head[i];~k;k=nxt[k])
            if (cost[k]&&d[edge[k]]+1<d[i])
                cur[i]=k,d[i]=d[edge[k]]+1;
                // d[i]=min(d[i],d[edge[k]]+1);
        ++gap[d[i]];
        // cur[i]=head[i];
        if (i!=vs)
            i=edge[prt[i]^1];
    }
    // cout<<"isap:"<<ans<<endl;
    return ans;
}

int mp[maxn];

pair<int,int> ans[maxn];

bool vis[maxn];

void dfs(int i)
{
    vis[i]=1;
    for (auto j:G[i])
    {
        if (vis[mp[j]]) continue;
        ans[j]=make_pair(i,mp[j]);
        dfs(mp[j]);
    }
}

int solve()
{
    if (isap()!=n-1)    return puts("-1");

    LL rt=1LL*n*(n+1)/2;
    for (int k=0;k<tot;k+=2)
    {
        int u=edge[k^1],v=edge[k];
        if (u==vs||v==vt||cost[k])   continue;
        rt-=u;
        mp[v-n]=u;
    }

    // cout<<rt<<endl;
    // for (int i=1;i<n;++i)
    //     cout<<i<<" "<<mp[i]<<endl;

    dfs(rt);
    for (int i=1;i<=n;++i)
        if (!vis[i])
            return puts("-1");
    for (int i=1;i<n;++i)
        printf("%d %d\n",ans[i].first,ans[i].second);
}

int main()
{
    init();
    solve();
    return 0;
}