There is a simple graph with an even number of edges. You need to represent it as a set of pairs of adjacent edges (having a common vertex).
Input
Input contains a sequence of the pairs with the integers. The length of the sequence is even and is from 2 to 100000. Each pair of integers is the identifiers of vertices of one edge. All the identifiers are from 1 to 100000. It is guaranteed that there are neither loops nor multiple edges in the given graph.
Output
If a required decomposition exists, in the first line output an integer m that is a number of pairs of adjacent edges.
The following m lines should contain triples of integers a, b, c, representing the edges of the given graph {a, b} and {b, c}.
If there is no such decomposition, output “1”.
Samples
input  output 

1 2
2 3
3 1
1 10
 2
1 2 3
3 1 10

1 2
2 3
3 1
4 10
 1 
Notes
Problem Author: Alexander Petrov, prepared by Alexander Ipatov