Separation
----------

In a network, a node that can disconnect the network
if it fails is called a `cut vertex' or `articulation
point'.  An edge that can disconnect the network if
it fails is called a `cut edge' or `bridge'.  More
specifically, an articulation point is a vertex of
a connected undirected graph which when removed, along
with all the edges of which it is an end point,
disconnects the graph.  And a bridge is an edge of a
connected undirected graph which when removed discon-
nects the graph.

You have been asked to find all the articulation points
and bridges of a very large network (undirected graph).


Input
-----

For each test case, first a line that gives the test
case name.  Then a line of the form

	M N

giving the number of vertices M and number of edges N.
Vertices are given identifiers 1, 2, 3, ..., M.  Then
N lines, one per edge, each of the form

	i j

specifying the the edge connects vertex i to vertex j.

Each edge appears only once.

	2 <= M <= 50,000
	1 <= N <= 1,000,000

Input terminates with an end of file.  The test case
name line is at most 80 characters.


Output
------

For each test case, first an exact copy of the test case
name line.  Then a line containing

	m n
	
where m is the number of articulation points and n is
the number of bridges.  This is followed by m lines, one
for each articulation point, each of the form

	i

where i is the vertex ID of the articulation point.
These lines MUST BE SORTED in order of increasing i.
Lastly there are n lines, one for each bridge, each
of the form

	i j

where the bridge connects vertices with IDs i and j.
Here i < j is REQUIRED, and the bridge lines MUST BE
SORTED in order of increasing i and for equal i in
order of increasing j.


Sample Input
------ -----

-- SAMPLE 1 --
2 1
1 2
-- SAMPLE 2 --
4 4
1 2
2 3
3 4
4 1
-- SAMPLE 3 --
4 3
1 2
2 3
3 4
-- SAMPLE 4 --
7 8
1 2
1 3
2 3
3 4
4 5
5 6
6 7
7 4
-- SAMPLE 5 --
9 9
1 2
2 3
3 4
4 5
5 6
6 1
7 1
8 3
9 5


Sample Output
------ ------

-- SAMPLE 1 --
0 1
1 2
-- SAMPLE 2 --
0 0
-- SAMPLE 3 --
2 3
2
3
1 2
2 3
3 4
-- SAMPLE 4 --
2 1
3
4
3 4
-- SAMPLE 5 --
3 3
1
3
5
1 7
3 8
5 9


File:	   separation.txt
Author:	   Bob Walton <walton@seas.harvard.edu>
Date:	   Sat Sep 16 01:28:30 EDT 2017

The authors have placed this file in the public domain;
they make no warranty and accept no liability for this
file.