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:
from collections import defaultdict
import sys
sys.setrecursionlimit(100000)

def seq():
    a = 1
    while True:
        yield a
        a += 1

def dfs(here, went, connect, discovery, low, answer, seq):
    went |= {here}
    discovery[here] = low[here] = next(seq)
    child = 0
    for con in connect[here]:
        if con not in went:
            parent[con] = here
            child += 1
            dfs(con, went, connect, discovery, low, answer, seq)
            low[here] = min(low[here], low[con])
            if discovery[here] < low[con]:
                answer[min(here,con)].append(max(here,con))
        elif parent[here] != con:
            low[here] = min(low[here], discovery[con])

vertices, edges = (int(n) for n in input().split(" "))
connect = defaultdict(list)
for _ in range(edges):
    v1, v2 = (int(n) for n in input().split(" "))
    connect[v1].append(v2)
    connect[v2].append(v1)
answer = defaultdict(list)
new_seq = seq()
went = set()
discovery = [0 for n in range(vertices)]
low = [float("inf") for n in range(vertices)]
parent = [None for n in range(vertices)]
dfs(0, went, connect, discovery, low, answer, new_seq)

for k in sorted(answer.keys()):
    for n in sorted(answer[k]):
        print(k,n)