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:
# Acceptance of input
import sys

f_i = sys.stdin

V, E = map(int, f_i.readline().split())

adj = [[] for i in range(V)]

for l_i in f_i:
    s, t = map(int, l_i.split())
    adj[s].append(t)
    adj[t].append(s)


# dfs traverse
prenum = [1] + [None] * (V - 1)
parent = [0] * V
lowest = [1] + [V] * (V - 1)

import collections

path = collections.deque()
path.append(0)

cnt = 1

while path:
    u = path[-1]
    adj_v = adj[u]
    for v in adj_v:
        if not prenum[v]:
            parent[v] = u
            path.append(v)
            cnt += 1
            prenum[v] = cnt
            lowest[v] = cnt
            adj[u].remove(v)
            adj[v].remove(u)
            break
    if u == path[-1]:
        for v in adj_v:
            lowest[u] = min(lowest[u], lowest[v])
            adj[u].remove(v)
            adj[v].remove(u)
        p = parent[u]
        lowest[p] = min(lowest[u], lowest[p])
        path.pop()


# output
bridge = []

for u in range(1, V):
    p = parent[u]
    if prenum[p] < lowest[u]:
        b = [p, u]
        b.sort()
        bridge.append(b)

bridge.sort()

for b in bridge:
    print(*b)