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(100000)

def dfs(v, tm):
    dts[v] = est[v] = tm + 1
    child = 0

    for i in adj[v]:
        if est[i] == float('inf'):
            child += 1
            parents[i] = v
            dfs(i, tm + 1)
            est[v] = min(est[v], est[i])

            if est[i] > dts[v]: 
                bridges.append((v, i)) if v < i else bridges.append((i, v))

        elif parents[v] != i:
            est[v] = min(est[v], dts[i])

nv, ne = map(int, input().split(' '))
adj = [[] for _ in range(nv)]
est = [float('inf')] * nv
parents = [None] * nv
dts = [0] * nv
bridges = []

for _ in range(ne):
    s, t = map(int, input().split(' '))
    adj[s].append(t)
    adj[t].append(s)

dfs(0, 0)
bridges.sort(key=lambda tup: (tup[0], tup[1]))
[print(str(bridge[0]) + ' ' + str(bridge[1])) for bridge in bridges]