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;
const int N=800005;
vector<int> bel[N];
int cur[N],from[N],S,T,ne[N],a[N],b[N],dis[N],flag[N],x,y,n,m,fi[N],tot,zz[N],sl[N];
queue<int>Q;
void jb(int x,int y,int z){
	ne[++tot]=fi[x];
	fi[x]=tot;
	zz[tot]=y;
	sl[tot]=z;
	ne[++tot]=fi[y];
	fi[y]=tot;
	zz[tot]=x;
	sl[tot]=0;
}
int bfs(){
	Q.push(S);
	memset(dis,-1,sizeof dis);
	dis[S]=0;
	while (!Q.empty()){
		int now=Q.front();Q.pop();
		for (int i=fi[now];i;i=ne[i])
			if (sl[i]&&dis[zz[i]]==-1){
				dis[zz[i]]=dis[now]+1;
				Q.push(zz[i]);
			}
	}
	return dis[T]!=-1;
}
int dfs(int x,int y){
	if (x==T)return y;
	int s=0,b;
	for (int &i=cur[x];i;i=ne[i])
		if (sl[i]&&dis[zz[i]]==dis[x]+1&&(b=min(sl[i],dfs(zz[i],min(sl[i],y))))){
			sl[i]-=b;
			sl[i^1]+=b;
			y-=b;
			s+=b;
			if (!y)return s;
		}
	return s;
}
int main(){
	scanf("%d",&n);
	S=0;T=2*n;
	tot=1;
	for (int i=1;i<n;i++){
		scanf("%d",&x);
		jb(S,i+n,1);
		while (x--){
			scanf("%d",&y);
			jb(i+n,y,1);
			bel[y].push_back(i);
		}
	}
	for (int i=1;i<=n;i++)jb(i,T,1);
	int ans=0;
	while (bfs()){
		for (int i=S;i<=T;i++)cur[i]=fi[i];
		ans+=dfs(S,1e9);
	}
	if (ans!=n-1){
		puts("-1");
		return 0;
	}
	for (int i=1;i<n;i++)
		for (int j=fi[i+n];j;j=ne[j])
			if (zz[j]&&!sl[j]){
				flag[zz[j]]=1;
				b[i]=zz[j];
			}
	for (int i=1;i<=n;i++)
		if (!flag[i])Q.push(i);
	ans=0;
	memset(flag,0,sizeof flag);
	while (!Q.empty()){
		int now=Q.front();Q.pop();
		ans++;
		for (int i=0;i<bel[now].size();i++)
			if (!flag[bel[now][i]]){
				flag[bel[now][i]]=1;
				a[bel[now][i]]=now;
				Q.push(b[bel[now][i]]);
			}
	}
	if (ans!=n){
		puts("-1");
		return 0;
	}
	for (int i=1;i<n;i++)printf("%d %d\n",a[i],b[i]);
}