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>
using namespace std;

vector<vector<int>> G;
vector<int> preorder;
vector<int> low;
using P = pair<int,int>;

void lowlink(int v,int prev, int &pre, vector<P>& ans){
  preorder[v]=pre;
  low[v]=pre;
  for(auto to:G[v]){
    if(preorder[to]==-1){
      lowlink(to,v,++pre,ans);
      if(low[to]==preorder[to]){
        ans.emplace_back(min(v,to),max(v,to));
      }
      low[v]=min(low[v],low[to]);
    }else if(to!=prev){
      low[v]=min(low[v],preorder[to]);
    }
  }
}

int main(){
  int V,E;
  cin>>V>>E;
  G.resize(V);
  preorder.resize(V,-1);
  low.resize(V);

  for(int i=0;i<E;i++){
    int s,t;
    cin>>s>>t;
    G[s].push_back(t);
    G[t].push_back(s);
  }
  int p=1;
  vector<P> ans;
  lowlink(0,-1,p,ans);
  sort(ans.begin(), ans.end());
  for(auto a:ans){
    cout<<a.first<<' '<<a.second<<endl;
  }
  // for(int i=0;i<V;i++){
  //   cout<<i<<' '<<preorder[i]<<' '<<low[i]<<endl;
  // }
}