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;

class LowLink
{
    using Graph = std::vector<std::vector<int>>;
    using P = std::pair<int, int>;
    std::vector<int> order;
    int next = 0;
    Graph G;
    std::set<P> bridges;

    void add(int a, int b)
    {
        bridges.insert(P(min(a, b), max(a, b)));
    }
    int dfs(int cur, int pre)
    {
        int res = order[cur] = next++;
        for (const auto &to : G[cur])
        {
            if (to == pre)
                continue;
            if (order[to] >= 0)
                res = std::min(res, order[to]);
            else
            {
                int low = dfs(to, cur);
                if (low > order[cur])
                    add(cur, to);
                res = std::min(res, low);
            }
        }
        return res;
    }

  public:
    LowLink(int _v) : G(_v, std::vector<int>()), order(_v, -1) {}
    void addEdge(int s, int t)
    {
        G[s].push_back(t);
    }
    std::set<P> bridge()
    {
        dfs(0, -1);
        return bridges;
    }
};

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    int V, E;
    cin >> V >> E;
    LowLink link(V);
    while (E--)
    {
        int s, t;
        cin >> s >> t;
        link.addEdge(s, t);
        link.addEdge(t, s);
    }
    auto st = link.bridge();
    for (auto p : st)
    {
        cout << p.first << " " << p.second << endl;
    }
}