Problem: Find bridges of an undirected graph G(V, E).

A bridge (also known as a cut-edge) is an edge whose deletion increase the number of connected components.

Constraints

* 1 ≤ |V| ≤ 100,000
* 0 ≤ |E| ≤ 100,000
* The graph is connected
* There are no parallel edges
* There are no self-loops

Input


|V| |E|
s0 t0
s1 t1
:
s|E|-1 t|E|-1


, where |V| is the number of nodes and |E| is the number of edges in the graph. The graph nodes are named with the numbers 0, 1,..., |V|-1 respectively.

si and ti represent source and target nodes of i-th edge (undirected).

Output

A list of bridges of the graph ordered by name. For each bridge, names of its end-ponints, source and target (source < target), should be printed separated by a space. The sources should be printed ascending order, then the target should also be printed ascending order for the same source.

Examples

Input

4 4
0 1
0 2
1 2
2 3


Output

2 3


Input

5 4
0 1
1 2
2 3
3 4


Output

0 1
1 2
2 3
3 4

Solution (in CPP):

Solution:
#include<iostream>
#include<vector>
#include<algorithm>
#include<climits>
using namespace std;

const int V_MAX=100000;
const int E_MAX=100000;

struct edge{
	int from;
	int to;
	bool operator<( const edge& right ) const {
        return from == right.from ? to < right.to : from < right.from;
    }
};

vector<int> G[V_MAX];
bool used_v[V_MAX]={};
//bool used_e[E_MAX][E_MAX]={};
vector<int> pre(V_MAX,INT_MAX);
vector<int> low(V_MAX,INT_MAX);
vector<edge> result;
int order;

void dfs(int s,int p){
	if(used_v[s]==true){return;}
	used_v[s]=true;
	pre[s]=order;
	low[s]=order;
	order++;
	for (int i=0;i<G[s].size();i++){
		//used_e[s][G[s][i]]=true;
		if(!used_v[G[s][i]]){
			dfs(G[s][i],s);
			low[s]=min(low[s],low[G[s][i]]);
		}else if(G[s][i]!=p){
			low[s]=min(low[s],pre[G[s][i]]);
		}
	}
	if(!(s==0 && p==0) && low[s]>pre[p]){
		edge e;
		e.from=min(s,p);
		e.to=max(s,p);
		result.push_back(e); 
	}
}

int main(){
	int V,E,s,t;
	cin>> V >> E;
	for (int i=0;i<E;i++){
		cin >> s >> t;
		G[s].push_back(t);
		G[t].push_back(s);
	}
	
	order=0;
	dfs(0,0);
	
	sort(result.begin(),result.end());
	for(int i=0;i<result.size();i++){
		cout << result[i].from << " " << result[i].to << endl;
	}
	/*
	for(int i=0;i<V;i++){
		cout << pre[i] << " ";
	}
	cout << endl;
	
	for(int i=0;i<V;i++){
		cout << low[i] << " ";
	}
	*/
	return 0;
}