Problem: 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}

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}

Examples

Input

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


Output

1 2
1 3
3 4
4 5


Input

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


Output

-1


Input

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


Output

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

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using lint = long long;
using pi = pair<int, int>;
const int MAXN = 100005;
const int MAXM = 100005;

struct bpm{
	vector<int> gph[MAXN];
	int dis[MAXN], l[MAXN], r[MAXM], vis[MAXN];
	void clear(){ for(int i=0; i<MAXN; i++) gph[i].clear();	}
	void add_edge(int l, int r){ gph[l].push_back(r); }
	bool bfs(int n){
		queue<int> que;
		bool ok = 0;
		memset(dis, 0, sizeof(dis));
		for(int i=0; i<n; i++){
			if(l[i] == -1 && !dis[i]){
				que.push(i);
				dis[i] = 1;
			}
		}
		while(!que.empty()){
			int x = que.front();
			que.pop();
			for(auto &i : gph[x]){
				if(r[i] == -1) ok = 1;
				else if(!dis[r[i]]){
					dis[r[i]] = dis[x] + 1;
					que.push(r[i]);
				}
			}
		}
		return ok;
	}
	bool dfs(int x){
		if(vis[x]) return 0;
		vis[x] = 1;
		for(auto &i : gph[x]){
			if(r[i] == -1 || (!vis[r[i]] && dis[r[i]] == dis[x] + 1 && dfs(r[i]))){
				l[x] = i; r[i] = x;
				return 1;
			}
		}
		return 0;
	}
	int match(int n){
		memset(l, -1, sizeof(l));
		memset(r, -1, sizeof(r));
		int ret = 0;
		while(bfs(n)){
			memset(vis, 0, sizeof(vis));
			for(int i=0; i<n; i++) if(l[i] == -1 && dfs(i)) ret++;
		}
		return ret;
	}
	bool chk[MAXN + MAXM];
	void rdfs(int x, int n){
		if(chk[x]) return;
		chk[x] = 1;
		for(auto &i : gph[x]){
			chk[i + n] = 1;
			rdfs(r[i], n);
		}
	}
	vector<int> getcover(int n, int m){ // solve min. vertex cover
		match(n);
		memset(chk, 0, sizeof(chk));
		for(int i=0; i<n; i++) if(l[i] == -1) rdfs(i, n);
		vector<int> v;
		for(int i=0; i<n; i++) if(!chk[i]) v.push_back(i);
		for(int i=n; i<n+m; i++) if(chk[i]) v.push_back(i);
		return v;
	}

}bpm;

int n, M[MAXN];
int proc[MAXN];
pi dap[MAXN];

vector<int> E[MAXN];
vector<int> R[MAXN];
queue<int> que;

int main(){
	scanf("%d",&n);
	for(int i=1; i<n; i++){
		int s;
		scanf("%d",&s);
		E[i].resize(s);
		for(auto &j : E[i]){
			scanf("%d",&j);
			R[j].push_back(i);
			if(j != 1) bpm.add_edge(i, j);
		}
	}
	int x = bpm.match(n + 1);
	if(x != n - 1){
		puts("-1");
		return 0;
	}
	for(int i=1; i<n; i++) M[i] = bpm.l[i];
	que.push(1);
	vector<pi> edg;
	while(!que.empty()){
		int x = que.front();
		que.pop();
		for(auto &j : R[x]){
			if(proc[j]) continue;
			proc[j] = 1;
			dap[j] = pi(M[j], x);
			que.push(M[j]);
		}
	}
	for(int i=1; i<n; i++) printf("%d %d\n", dap[i].first, dap[i].second);
}