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 int long long
typedef vector<int>vint;
typedef pair<int,int>pint;
typedef vector<pint>vpint;
#define rep(i,n) for(int i=0;i<(n);i++)
#define reps(i,f,n) for(int i=(f);i<(n);i++)
#define all(v) (v).begin(),(v).end()
#define each(it,v) for(__typeof((v).begin()) it=(v).begin();it!=(v).end();it++)
#define pb push_back
#define fi first
#define se second
template<typename A,typename B>inline void chmin(A &a,B b){if(a>b)a=b;}
template<typename A,typename B>inline void chmax(A &a,B b){if(a<b)a=b;}

int N,M;
vint G[111111];
bool vis[111111];
int ord[111111],low[111111];
vpint bridge;
void dfs(int v,int p,int &k){
    ord[v]=k++;
    low[v]=ord[v];
    vis[v]=true;
    for(auto u:G[v]){
        if(vis[u]){
            if(u!=p)chmin(low[v],ord[u]);
        }
        else{
            dfs(u,v,k);
            if(ord[v]<low[u])bridge.pb({min(v,u),max(v,u)});
            chmin(low[v],low[u]);
        }
    }
}

signed main(){
    cin>>N>>M;
    rep(i,M){
        int a,b;cin>>a>>b;
        G[a].pb(b);G[b].pb(a);
    }
    int k=0;dfs(0,-1,k);
    sort(all(bridge));
    rep(i,bridge.size())cout<<bridge[i].fi<<" "<<bridge[i].se<<endl;
}