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 PYTHON3):

Solution:
import sys
sys.setrecursionlimit(10 ** 8)


def lowLink(N: int, Adj: list):
	articulation = []
	bridge = []
	order = [None] * N
	lowest = [1 << 100] * N

	def _dfs(cur, pre, k):
		order[cur] = lowest[cur] = k
		is_articulation = False
		cnt = 0
		for nxt in Adj[cur]:
			if order[nxt] is None:
				cnt += 1
				_dfs(nxt, cur, k + 1)
				if lowest[cur] > lowest[nxt]:
					lowest[cur] = lowest[nxt]
				is_articulation |= pre >= 0 and lowest[nxt] >= order[cur]
				if order[cur] < lowest[nxt]:
					if cur < nxt:
						bridge.append((cur, nxt))
					else:
						bridge.append((nxt, cur))
			elif nxt != pre and lowest[cur] > order[nxt]:
				lowest[cur] = order[nxt]
		is_articulation |= pre < 0 and cnt > 1
		if is_articulation:
			articulation.append(cur)

	_dfs(0, -1, 0)
	return articulation, bridge


def main():
	n, m, *L = map(int, open(0).read().split())
	adj = [[] for _ in range(n)]
	for s, t in zip(*[iter(L)] * 2):
		adj[s] += t,
		adj[t] += s,
	_, bridge = lowLink(n, adj)
	for x, y in sorted(bridge):
		print(x, y)


if __name__ == '__main__':
	main()