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<vector>
#include<algorithm>
using namespace std;

typedef pair<int,int> pii;
struct LowLink{
    int n, k;   // k  
    vector<int> ord, low;
    vector<pii> edge;
    vector<vector<int>> v;
    vector<bool> vis;

    LowLink(int n) : n(n){
        ord.resize(n);
        v.resize(n);
        low.resize(n);
        vis.resize(n, 0);
    }

    void add_edge(int a, int b){
        edge.push_back({a, b});
        v[a].push_back(b);
        v[b].push_back(a);
    }

    void dfs(int x, int p, int &k){
        ord[x] = low[x] = k++;
        vis[x] = true;
        for(int j : v[x]){
            if(vis[j]){
                if(j != p)  low[x] = min(low[x], ord[j]);
            }else{
                dfs(j, x, k);
                low[x] = min(low[x], low[j]);
            }
        }
    }

    void build(){
        k = 0;
        dfs(0, -1, k);
    }

    vector<pii> bridge(){
        vector<pii> ret;
        for(pii p : edge){
            int x = p.first, y = p.second;
            if(ord[x] > ord[y]) swap(x, y);
            if(ord[x] < low[y]) ret.push_back(p);
        }
        return ret;
    }
};

int main(){
    int n, m;
    cin >> n >> m;
    LowLink l(n);
    while(m--){
        int u, v;
        cin >> u >> v;
        if(u > v)   swap(u, v);
        l.add_edge(u, v);
    }
    l.build();
    vector<pii> res = l.bridge();
    sort(res.begin(), res.end());
    for(pii p : res){
        cout << p.first << " " << p.second << endl;
    }
    return 0;
}