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;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; }

using Lint=long long;
using Graph=vector<vector<int>>;

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    int N,M; cin>>N>>M;
    Graph G(N);
    for(int i=0;i<M;i++){
        int a,b; cin>>a>>b;
        G[a].push_back(b);
        G[b].push_back(a);
    }

    vector<int> ord(N,-1),sum(N);
    vector<pair<int,int>> bridges;
    function<void(int,int)> dfs=[&](int v,int p)
    {
        static int order=0;
        ord[v]=order++;
        for(int u:G[v]) if(u!=p){
            if(ord[u]<0){
                dfs(u,v);
                sum[v]+=sum[u];
                if(sum[u]==0) bridges.push_back(minmax(v,u));
            }else if(ord[v]>ord[u]){
                // cout<<v+1<<' '<<u+1<<endl;
                sum[v]++; sum[u]--;
            }
        }
    };
    dfs(0,-1);
    sort(bridges.begin(),bridges.end());
    for(auto p:bridges) cout<<p.first<<' '<<p.second<<endl;
    return 0;
}