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 <queue>
#include <stack>
#include <algorithm>

#define FOR(i,n) for(int i=0; i<n; i++)

using namespace std;
struct Edge {
    int u;
    int v;
};
bool operator< (const Edge& e1, const Edge& e2) {
    return e1.u < e2.u || (e1.u == e2.u && e1.v < e2.v);
};
typedef vector<vector<int> > Graph;

void DFS(Graph &g, int u, int &clock, vector<int> &low, vector<int> &disc, vector<bool> &seen, vector<int> &parent, vector<Edge> &bridges) {
    stack<int> s;
    for(int v: g[u]) {
        if (! seen[v]) {
            clock++;

            disc[v] = clock;
            low[v] = clock;
            seen[v] = true;
            parent[v] = u;

            DFS(g, v, clock, low, disc, seen, parent, bridges);

            low[u] = min(low[u], low[v]);

            if (low[v] > disc[u])
                bridges.push_back(Edge{min(u, v), max(u, v)});
        } else if (v != parent[u]) {
            low[u]  = min(low[u], disc[v]);
        }
    }
}

int main () {
    int V, E;
    cin >> V >> E;

    Graph g(V);
    vector<Edge> bridges;

    FOR(i,E) {
        int s, t;
        cin >> s >> t;

        g[s].push_back(t);
        g[t].push_back(s);
    }
    int clock = 2;
    vector<int> low(V, 0);
    vector<int> disc(V, 0);
    vector<int> parent(V, -1);
    vector<bool> seen(V, false);
    disc[0] = 1;
    low[0] = 1;
    seen[0] = true;

    DFS(g, 0, clock, low, disc, seen, parent, bridges);

    sort(bridges.begin(), bridges.end());

    for(Edge e: bridges)
        cout << e.u << " " << e.v << endl;
}