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;

int n;
vector<vector<int>> graph;
vector<int> ord, low;
vector<pair<int, int>> bridge;

void dfs(int v, int p, int& k) {
    ord[v] = low[v] = k++;
    for (int u : graph[v]) {
        if (u == p) continue;
        else if (ord[u] == -1) {
            dfs(u, v, k);
            low[v] = min(low[v], low[u]);
            if (low[u] == ord[u]) {
                bridge.emplace_back(v, u);
            }
        }
        else {
            low[v] = min(low[v], low[u]);
        }
    }
}

void build() {
    ord.assign(n, -1);
    low.resize(n);

    int k = 0;
    dfs(0, -1, k);
}

int main() {
    int V, E;
    cin >> V >> E;
    graph.resize(V);
    for (int i = 0; i < E; ++i) {
        int s, t;
        cin >> s >> t;
        graph[s].push_back(t);
        graph[t].push_back(s);
    }

    n = V;
    build();
    for (auto&& e : bridge) {
        if (e.first > e.second) swap(e.first, e.second);
    }
    sort(bridge.begin(), bridge.end());
    for (auto&& e : bridge) {
        cout << e.first << ' ' << e.second << endl;
    }
}