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<(int)(n);i++)
using namespace std;
using ll = long long ;
using P = pair<int,int> ;
using pll = pair<long long,long long>;
constexpr int INF = 1e9;
constexpr long long LINF = 1e17;
constexpr int MOD = 1000000007;
constexpr double PI = 3.14159265358979323846;
int v = 100005,e;
int c = 0;
vector<vector<int>> graph(v,vector<int>());
vector<bool> seen(v,false);
vector<int> ord(v);
vector<int> low(v);
vector<P> bridges;

void dfs(int i,int par=-1){
    seen[i] = true;
    ord[i] = low[i] = c++;

    for(int j:graph[i]){
        if(!seen[j]){
            dfs(j,i);
            low[i] = min(low[i],low[j]);
            if(ord[i] < low[j]) bridges.push_back(P(min(i,j),max(i,j)));
        }else if(j!=par){
            low[i] = min(low[i],ord[j]);
        }
    }

    return;
}

int main(){
    cin >> v >> e;
    rep(i,e){
        int s,t;
        cin >> s >> t;
        graph[s].push_back(t);
        graph[t].push_back(s);
    }
    dfs(0);
    sort(bridges.begin(),bridges.end());
    for(P p:bridges){
        cout << p.first << " " << p.second << endl;
    }
    return 0;
}