#include <bits/stdc++.h>

using namespace std;

template< typename T >
struct edge {
  int src, to;
  T cost;

  edge(int to, T cost) : src(-1), to(to), cost(cost) {}

  edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}

  edge &operator=(const int &x) {
    to = x;
    return *this;
  }

  operator int() const { return to; }
};

template< typename T >
using Edges = vector< edge< T > >;
template< typename T >
using WeightedGraph = vector< Edges< T > >;
using UnWeightedGraph = vector< vector< int > >;
template< typename T >
using Matrix = vector< vector< T > >;


template< typename G >
struct LowLink {
  const G &g;
  vector< int > used, ord, low;
  vector< int > articulation;
  vector< pair< int, int > > bridge;

  LowLink(const G &g) : g(g), used(g.size()), ord(g.size()), low(g.size()) {}

  int build(int idx = 0, int k = 0, int par = -1) {
    used[idx] = true;
    ord[idx] = k++;
    low[idx] = ord[idx];
    bool is_articulation = false;
    int cnt = 0, ordmax = k;
    for(auto &to : g[idx]) {
      if(!used[to]) {
        ++cnt;
        ordmax = build(to, ordmax, idx);
        low[idx] = min(low[idx], low[to]);
        is_articulation |= ~par && low[to] >= ord[idx];
        if(ord[idx] < low[to]) bridge.emplace_back(minmax(idx, to));
      } else if(to != par) {
        low[idx] = min(low[idx], ord[to]);
      }
    }
    is_articulation |= par == -1 && cnt > 1;
    if(is_articulation) articulation.push_back(idx);
    return ordmax;
  }
};


int main() {
  int V, E;
  scanf("%d %d", &V, &E);
  UnWeightedGraph g(V);
  for(int i = 0; i < E; i++) {
    int x, y;
    scanf("%d %d", &x, &y);
    g[x].push_back(y);
    g[y].push_back(x);
  }
  LowLink< UnWeightedGraph > lowlink(g);
  lowlink.build();
  sort(lowlink.bridge.begin(), lowlink.bridge.end());
  for(auto &p : lowlink.bridge) printf("%d %d\n", p.first, p.second);
}


### Prompt

Your challenge is to write a Cpp solution to the following 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

### Response

```cpp
#include <bits/stdc++.h>

using namespace std;

template< typename T >
struct edge {
  int src, to;
  T cost;

  edge(int to, T cost) : src(-1), to(to), cost(cost) {}

  edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}

  edge &operator=(const int &x) {
    to = x;
    return *this;
  }

  operator int() const { return to; }
};

template< typename T >
using Edges = vector< edge< T > >;
template< typename T >
using WeightedGraph = vector< Edges< T > >;
using UnWeightedGraph = vector< vector< int > >;
template< typename T >
using Matrix = vector< vector< T > >;


template< typename G >
struct LowLink {
  const G &g;
  vector< int > used, ord, low;
  vector< int > articulation;
  vector< pair< int, int > > bridge;

  LowLink(const G &g) : g(g), used(g.size()), ord(g.size()), low(g.size()) {}

  int build(int idx = 0, int k = 0, int par = -1) {
    used[idx] = true;
    ord[idx] = k++;
    low[idx] = ord[idx];
    bool is_articulation = false;
    int cnt = 0, ordmax = k;
    for(auto &to : g[idx]) {
      if(!used[to]) {
        ++cnt;
        ordmax = build(to, ordmax, idx);
        low[idx] = min(low[idx], low[to]);
        is_articulation |= ~par && low[to] >= ord[idx];
        if(ord[idx] < low[to]) bridge.emplace_back(minmax(idx, to));
      } else if(to != par) {
        low[idx] = min(low[idx], ord[to]);
      }
    }
    is_articulation |= par == -1 && cnt > 1;
    if(is_articulation) articulation.push_back(idx);
    return ordmax;
  }
};


int main() {
  int V, E;
  scanf("%d %d", &V, &E);
  UnWeightedGraph g(V);
  for(int i = 0; i < E; i++) {
    int x, y;
    scanf("%d %d", &x, &y);
    g[x].push_back(y);
    g[y].push_back(x);
  }
  LowLink< UnWeightedGraph > lowlink(g);
  lowlink.build();
  sort(lowlink.bridge.begin(), lowlink.bridge.end());
  for(auto &p : lowlink.bridge) printf("%d %d\n", p.first, p.second);
}


```