Given an undirected graph containing N vertices and M edges, find all the articulation points and all the bridges in the graph.

Input:
First line consists of two space separated integers denoting N and M. M lines follow, each containing two space separated integers X and Y denoting there is an edge between X and Y.

Output:
If the number of articulation points in the graph is p and that of bridges is q , then print as shown below:
p
p space separated integers, the articulation points, sorted in increasing order
q
q lines, each containing two space separated integers, the bridges in the graph. For a bridge u-v, print u first if u < v, otherwise print v first. Print all the bridges in increasing order of first vertex, and if first vertex is same, then in increasing order of second vertex.

Constraints:
1 ≤ N, M ≤ 10
0 ≤ X, Y ≤ N-1