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

from collections import deque
sys.setrecursionlimit(1000000)


def dfs(current, prev):
    global time
    # node currentを訪問した直後の処理
    ord[current] = time
    low[current] = time
    time += 1
    color[current] = BLACK

    for next in G[current]:
        if color[next] == WHITE:
            # node currentからnode nextへ訪問する直前の処理
            parent[next] = current
            dfs(next, current)

            # node nextの探索が終了した直後の処理
            low[current] = min(low[current], low[next])
        elif next != prev:
            # edge current --> next がback-edgeの場合の処理
            low[current] = min(low[current], ord[next])


def bridge():
    global time
    time = 1
    dfs(0, -1)  # 0をrootとしてlowの計算
    for u, v in edges:
        if ord[u] < low[v] or ord[v] < low[u]:
            br.add((u, v))


G = {}
edges = set([])
br = set([])
v, n = map(int, input().split())
for i in range(0, v):
    G[i] = []
for i in range(n):
    s, t = map(int, input().split())
    G[s].append(t)
    G[t].append(s)
    edges.add((s, t))
WHITE = 0
BLACK = 2

color = [WHITE] * (v)
parent = [0] * (v)
ord = [0] * (v)
low = [0] * (v)
parent = [0] * (v)
bridge()
if br:
    br = list(map(sorted, br))
    br.sort(key=lambda x: x[1])
    br.sort(key=lambda x: x[0])
    # 安定ソートだからこれができる
    for ans in br:
        print(*ans)