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>
using namespace std;
#include<vector>
#include<algorithm>
struct bridge{
	vector<int>ord,low;
	vector<bool>art;
	vector<pair<int,int> >bridges;
	vector<vector<int> >G;
	bridge(int n_=0):ord(n_,-1),low(n_),art(n_,false),G(n_){}
	void add_edge(int u,int v)
	{
		G[u].push_back(v);
		G[v].push_back(u);
	}
	bool operator[](int a){return art[a];}
	void dfs(int u,int p,int&cnt)
	{
		low[u]=ord[u]=cnt++;
		for(int&v:G[u])
		{
			if(ord[v]==-1)
			{
				dfs(v,u,cnt);
				low[u]=min(low[u],low[v]);
				art[u]=art[u]|ord[u]<=low[v];
				if(ord[u]<low[v])bridges.push_back(u<v?make_pair(u,v):make_pair(v,u));
			}
			else if(v!=p)
			{
				low[u]=min(low[u],ord[v]);
			}
		}
	}
	void build()
	{
		int k=1,cnt=0;
		low[0]=ord[0]=0;
		for(int&v:G[0])if(ord[v]==-1)
		{
			dfs(v,0,k);
			if(ord[0]<low[v])bridges.push_back(make_pair(0,v));
			cnt++;
		}
		if(cnt>=2)art[0]=true;
	}
};

int main()
{
	int n,m;cin>>n>>m;
	bridge P(n);
	for(int i=0;i<m;i++)
	{
		int a,b;cin>>a>>b;
		P.add_edge(a,b);
	}
	P.build();
	sort(P.bridges.begin(),P.bridges.end());
	for(int i=0;i<P.bridges.size();i++)cout<<P.bridges[i].first<<" "<<P.bridges[i].second<<endl;
}