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<string>
#include<algorithm>
#include<vector>
#include<iomanip>
#include<math.h>
#include<complex>
#include<queue>
#include<deque>
#include<map>
#include<set>
#include<bitset>
using namespace std;
#define REP(i,m,n) for(int i=(int)m ; i < (int) n ; i++ )
#define rep(i,n) REP(i,0,n)
typedef long long ll;
typedef pair<int,int> pint;
typedef pair<ll,int> pli;
const int inf=1e9+7;
const ll longinf=1LL<<60 ;
const ll mod=1e9+7 ;
int dx[4]={1,0,-1,0} , dy[4]={0,1,0,-1} ;

typedef vector<vector<int>> graph;
struct LowLink{
    graph v;
    vector<int> art,low,ord;
    vector <pint> bridge;

    LowLink(int n):v(n),ord(n,-1),low(n){};

    void addedge(int x,int y){
        v[x].push_back(y);
        v[y].push_back(x);
    }
    
    void dfs(int& count,int from,int x){
        ord[x]=count++;
        low[x]=ord[x];
        bool isart=false;
        int cnt=0;
        for(auto to:v[x]){
            if(to==from)continue;
            if(ord[to]==-1){
                cnt++;
                dfs(count,x,to);
                if(ord[x]<low[to])bridge.push_back({min(x,to),max(to,x)});
                if(from!=-1&&ord[x]<=low[to])isart=true;
                low[x]=min(low[x],low[to]);
            }
            else low[x]=min(low[x],ord[to]);
        }
        if(from==-1&&cnt>1)isart=true;
        if(isart)art.push_back(x);
    }
    void dfs(){
        int count=0;
        dfs(count,-1,0);
    }
};


int main(){
    int n,m;
    cin>>n>>m;
    LowLink ll(n);
    rep(i,m){
        int x,y;
        cin>>x>>y;
        ll.addedge(x,y);
    }
    ll.dfs();
    sort(ll.bridge.begin(),ll.bridge.end());
    for(auto x:ll.bridge)cout<<x.first<<" "<<x.second<<endl;
   return 0;
}