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;
inline bool chmin (int& a, int b) {
	if (a > b) {
		a = b;
		return true;
	}
	return false;
}
int main() {
	int n, m;
	cin >> n >> m;
	vector<vector<int>> grh(n);
	for (int i = 0; i < m; i++) {
		int s, t;
		cin >> s >> t;
		grh[s].push_back(t);
		grh[t].push_back(s);
	}
	int tmr = 0;
	vector<int> ord(n, -1), low(n, -1);
	vector<pair<int, int>> bdg;
	function<void(int, int)> dfs = [&] (
		int crr
	,	int prt
	) {
		ord[crr] = low[crr] = tmr++;
		for (int nxt : grh[crr]) {
			if (ord[nxt] == -1) dfs(nxt, crr);
			if (nxt != prt) chmin(low[crr], low[nxt]);
			if (ord[crr] < low[nxt]) bdg.emplace_back(crr, nxt);
		}
	};
	dfs(0, 0);
	for (auto it = bdg.begin(); it != bdg.end(); it++) {
		if (it->first > it->second) swap(it->first, it->second);
	}
	sort(bdg.begin(), bdg.end());
	for (auto it = bdg.begin(); it != bdg.end(); it++) {
		cout << it->first << ' ' << it->second << '\n';
	}
	cout << flush;
	return 0;
}