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;
 
typedef pair<int,int> ii;

const int MAXN = 100000;

int N, E, num[MAXN], low[MAXN], cnt = 1;
bool vis[MAXN];
vector<int> adjList[MAXN];
vector<ii> ans;
 
void dfs(int u, int par) {
    vis[u] = true;
    low[u] = num[u] = cnt++;
    for (int i = 0; i < adjList[u].size(); i++) {
        int v = adjList[u][i];

        if (!vis[v]) {
            dfs(v, u);
            if (low[v] > num[u]) {
                int s = min(v, u);
                int t = max(v, u);
                ans.push_back(ii(s,t));
            }
            low[u] = min(low[u], low[v]);
        }
        else if (v != par) low[u] = min(low[u], num[v]);
    }
}
     
 
int main() {

    scanf("%d%d",&N,&E);
    for (int i = 0, u, v; i < E; i++) {
        scanf("%d%d",&u,&v);

        adjList[u].push_back(v);
        adjList[v].push_back(u);
    }
 
    dfs(0, 0);
 
    sort(ans.begin(), ans.end());
    for (int i = 0; i < ans.size(); i++)
        printf("%d %d\n", ans[i].first, ans[i].second);

    return 0;
}