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 rep(i,n)for(int i=0;i<(n);i++)
using namespace std;
typedef pair<int,int>P;
 
vector<int>E[100000];
int s[100000],t[100000];
int dep[100000],low[100000],k;
bool used[100000];
vector<P>V;
 
void dfs(int v,int p,int d){
    used[v]=true;
    low[v]=dep[v]=d;
    for(auto u:E[v]){
        if(!used[u]){
            dfs(u,v,d+1);
            low[v]=min(low[v],low[u]);
            if(dep[v]<low[u])V.push_back(P(min(u,v),max(u,v)));
        }
        else if(p!=u){
            low[v]=min(low[v],dep[u]);
        }
    }
}
int main(){
    int v,e;scanf("%d%d",&v,&e);
    rep(i,e){
        scanf("%d%d",&s[i],&t[i]);
        E[s[i]].push_back(t[i]);
        E[t[i]].push_back(s[i]);
    }
    dfs(0,-1,0);
    sort(V.begin(),V.end());
    for(auto p:V){
        cout<<p.first<<' '<<p.second<<endl;
    }
}