// Verified @ GRL_3_A

#include <bits/stdc++.h>
using namespace std;

typedef unsigned long long ull;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<double, double> pdd;
const ull mod = 1e9 + 7;
#define REP(i,n) for(int i=0;i<(int)n;++i)

//debug
#define dump(x)  cerr << #x << " = " << (x) << endl;
#define debug(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ")" << " " << __FILE__ << endl;

template < typename T >
void vprint(T &v, int size){
	REP(i, size){
		cout << v[i] << " ";
	}
	cout << endl;
}

ll N, M;
vector<ll> G[101010];
vector<ll> dfs_tree[101010];
vector<ll> low(101010);
vector<ll> ord(101010, -1);
ll cnt = 0;

void dfs(ll now, ll par){
	ord[now] = cnt;
	cnt++;
	low[now] = ord[now];
	REP(i, G[now].size()){
		ll next = G[now][i];
		if(ord[next] == -1){
			dfs_tree[now].push_back(next);
			dfs(next, now);
			low[now] = min(low[now], low[next]);
		}else if(next != par){
			low[now] = min(low[now], ord[next]);
		}
	}
	return;
}

vector<pll> enum_bridge(){
	// construct lowlink
	ll root = 0;
	dfs(root, -1);

	// enumerate bridge
	vector<pll> res;
	REP(i, N){
		REP(j, dfs_tree[i].size()){
			if(ord[i] < low[dfs_tree[i][j]]){
				res.push_back({i, dfs_tree[i][j]});
			}
		}
	}
	return res;
}

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

    cin >> N >> M;
    REP(i, M){
    	int s, t;
    	cin >> s >> t;
    	G[s].push_back(t);
    	G[t].push_back(s);
    }

    auto res = enum_bridge();
    REP(i, res.size()) if(res[i].first > res[i].second) swap(res[i].first, res[i].second);
    sort(res.begin(), res.end());
    REP(i, res.size()){
    	cout << res[i].first << " " << res[i].second << endl;
    }

    //vprint(low, N);
    //vprint(ord, N);
    return 0;
}

### Prompt

Develop a solution in CPP to the problem described below:

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
// Verified @ GRL_3_A

#include <bits/stdc++.h>
using namespace std;

typedef unsigned long long ull;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<double, double> pdd;
const ull mod = 1e9 + 7;
#define REP(i,n) for(int i=0;i<(int)n;++i)

//debug
#define dump(x)  cerr << #x << " = " << (x) << endl;
#define debug(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ")" << " " << __FILE__ << endl;

template < typename T >
void vprint(T &v, int size){
	REP(i, size){
		cout << v[i] << " ";
	}
	cout << endl;
}

ll N, M;
vector<ll> G[101010];
vector<ll> dfs_tree[101010];
vector<ll> low(101010);
vector<ll> ord(101010, -1);
ll cnt = 0;

void dfs(ll now, ll par){
	ord[now] = cnt;
	cnt++;
	low[now] = ord[now];
	REP(i, G[now].size()){
		ll next = G[now][i];
		if(ord[next] == -1){
			dfs_tree[now].push_back(next);
			dfs(next, now);
			low[now] = min(low[now], low[next]);
		}else if(next != par){
			low[now] = min(low[now], ord[next]);
		}
	}
	return;
}

vector<pll> enum_bridge(){
	// construct lowlink
	ll root = 0;
	dfs(root, -1);

	// enumerate bridge
	vector<pll> res;
	REP(i, N){
		REP(j, dfs_tree[i].size()){
			if(ord[i] < low[dfs_tree[i][j]]){
				res.push_back({i, dfs_tree[i][j]});
			}
		}
	}
	return res;
}

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

    cin >> N >> M;
    REP(i, M){
    	int s, t;
    	cin >> s >> t;
    	G[s].push_back(t);
    	G[t].push_back(s);
    }

    auto res = enum_bridge();
    REP(i, res.size()) if(res[i].first > res[i].second) swap(res[i].first, res[i].second);
    sort(res.begin(), res.end());
    REP(i, res.size()){
    	cout << res[i].first << " " << res[i].second << endl;
    }

    //vprint(low, N);
    //vprint(ord, N);
    return 0;
}

```