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<bits/stdc++.h>
using namespace std;
#define pb push_back
#define fi first
#define sc second
#define mp make_pair
#define ps push
#define fr front
typedef pair<int,int> pii;

#define MAX_N 100000

int ord[MAX_N],low[MAX_N];
vector<int> g[MAX_N];
bool f[MAX_N];
vector<pii> ans;

void dfs(int u,int v,int k){
	f[v]=true;
	ord[v]=k;
	low[v]=ord[v];
	for(int j=0;j<g[v].size();++j){
		int w=g[v][j];
		if(w==u) continue;
		else if(f[w]) low[v]=min(low[v],ord[w]);
		else{
			dfs(v,w,k+1);
			low[v]=min(low[v],low[w]);
			if(ord[v]<low[w]) ans.pb(mp(min(v,w),max(v,w)));
		}
	}
}

int main(){
	int n,e;
	scanf("%d%d",&n,&e);
	vector<pii> es;
	for(int j=0;j<e;++j){
		int v,w;
		scanf("%d%d",&v,&w);
		g[v].pb(w);
		g[w].pb(v);
	}
	fill(f,f+n,false);
	dfs(0,0,0);
	sort(ans.begin(),ans.end());
	for(int j=0;j<ans.size();++j) printf("%d %d\n",ans[j].fi,ans[j].sc); 
}