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 INF 100010
typedef pair<int,int> P;
vector<int> G[100010];
int V,E;
int ord[100010];
int low[100010];

int lowlink(int x,int p,int n){
  if(ord[x]==INF)ord[x]=n;
  else return ord[x];
  int ans=INF;
  for(int i=0;i<G[x].size();i++){
    if(G[x][i]==p)continue;
    ans=min(ans,lowlink(G[x][i],x,n+1));
  }
  return low[x]=ans;
}

int main(){
  for(int i=0;i<100010;i++)
    low[i]=ord[i]=INF;
  cin>>V>>E;
  P p[100010];
  for(int i=0;i<E;i++){
    int s,t;
    cin>>s>>t;
    G[s].push_back(t);
    G[t].push_back(s);
    if(s>t)swap(s,t);
    p[i]=P(s,t);
  }
  sort(p,p+E);
  lowlink(0,-1,0);
  for(int i=0;i<E;i++){
    int f=0;
    int u=p[i].first,v=p[i].second;
    if(ord[u]>ord[v])swap(u,v);
    if(ord[u]<low[v])cout<<p[i].first<<" "<<p[i].second<<endl;
  }
  return 0;
}