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:
#!/usr/bin/env python3
# N,M = map(int,sys.stdin.readline().split())
# a = tuple(map(int,sys.stdin.readline().split())) # single line with multi param
# a = tuple(int(sys.stdin.readline()) for _ in range(N)) # multi line with single param
# a = tuple(tuple(map(int,sys.stdin.readline().rstrip().split())) for _ in range(N)) # multi line with multi param
# s = sys.stdin.readline().rstrip()
# N = int(sys.stdin.readline())
# INF = float("inf")

import sys,collections
sys.setrecursionlimit(100000)

INF = float("inf")

V,E = map(int,sys.stdin.readline().split())
st = tuple(tuple(map(int,sys.stdin.readline().rstrip().split())) for _ in range(E)) # multi line with multi param

G = [[] for _ in range(V)]

for s,t in st:
    G[s].append(t)
    G[t].append(s) #not directed

visited = set()
prenum = [0]*V
parent = [0]*V
lowest = [0]*V
timer = 0

def dfs(current,prev):
    global timer
    parent[current]=prev
    prenum[current]=lowest[current]=timer
    timer += 1
    visited.add(current)
    for nex in G[current]:
        if not nex in visited:
            dfs(nex,current)
            lowest[current]=min(lowest[current],lowest[nex])
        elif nex != prev:
            lowest[current]=min(lowest[current],prenum[nex])
dfs(0,-1)
ret = []

for i in range(1,V):
    p = parent[i]
    if prenum[p] < lowest[i]:
        if p < i:
            ret.append([p,i])
        else:
            ret.append([i,p])
ret = sorted(list(ret))

for s,t in ret:
    print(s,t)