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>
#define pb push_back
#define ff first
#define ss second
using namespace std;
typedef pair<int,int> pii;
const int N=100005;

int n,m,tot;
int vis[N],low[N];
vector<int>G[N];
vector<pii>ans;

void dfs(int u,int p) {
    vis[u]=low[u]=++tot;
    for (int v:G[u]) {
        if (v == p) continue;
        if (!vis[v]) {
            dfs(v,u);
            low[u]=min(low[u],low[v]);
            if (low[v]>vis[u]) ans.pb({min(u,v),max(u,v)});
        }
        low[u]=min(low[u],vis[v]);
    }
}

int main() {
    ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0);
    cin>>n>>m;
    while (m--) {
        int u,v; cin>>u>>v,
        G[u].pb(v),
        G[v].pb(u);
    }
    for (int i=0;i<n;++i) if (!vis[i]) dfs(i,-1);
    sort(ans.begin(),ans.end());
    for (auto p:ans) cout<<p.ff<<' '<<p.ss<<'\n';
}