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>
#define ll long long
#define INF 999999999
#define MOD 1000000007
#define rep(i,n) for(int i=0;i<n;i++)

using namespace std;

typedef pair<int,int>P;

const int MAX_N = 100000;

vector<int> G[MAX_N];
vector<pair<int, int> > bridge;
int ord[MAX_N];	//?¨??????????
int low[MAX_N]; //low[u]???u????????????1???????????????????????£?????????????????????????????????ord???????°????
bool visit[MAX_N]; //?¨?????????????????????????????????°

void dfs(int v,int p,int &k) //&??????????????¨??§k???????????§?????? p???v??????
{
	visit[v] = true;
	ord[v] = k++;
	low[v] = ord[v];
	for(int i=0;i<G[v].size();i++){
		if(!visit[G[v][i]]){
			dfs(G[v][i],v,k);
			low[v] = min(low[v],low[G[v][i]]);	//??????????????????low??¨????????????
			if(ord[v] < low[G[v][i]]){
				bridge.push_back(make_pair(min(v,G[v][i]), max(v,G[v][i])));
			}
		}else if(G[v][i] != p){
			low[v] = min(low[v],ord[G[v][i]]); //???????????§????????£??????????¨????????????¨????????????
		}
	}
}

int main()
{
	int n,m;
	scanf("%d %d",&n,&m);
	for(int i=0;i<m;i++){
		int x,y;
		scanf("%d %d",&x,&y);
		G[x].push_back(y);
		G[y].push_back(x);
	}
	int k = 0;
	fill(visit,visit+n,false);
	for(int i=0;i<n;i++){
		if(!visit[i]) dfs(i,-1,k);
	}
	sort(bridge.begin(), bridge.end());
	for(int i=0;i<bridge.size();i++){
		printf("%d %d\n",bridge[i].first,bridge[i].second);
	}
}