CF589H Tourist Guide

It is not that easy to create a tourist guide as one might expect. A good tourist guide should properly distribute flow of tourists across the country and maximize the revenue stream from the tourism. This is why there is a number of conditions to be met before a guide may be declared as an official tourist guide and approved by Ministry of Tourism. Ministry of Tourism has created a list of $ k $ remarkable cities out of $ n $ cities in the country. Basically, it means that in order to conform to strict regulations and to be approved by the ministry a tourist guide should be represented as a set of routes between remarkable cities so that the following conditions are met: - the first and the last city of every route are distinct remarkable cities, - each remarkable city can be an endpoint of at most one route, - there is no pair of routes which share a road. Please note that a route may pass through a remarkable city. Revenue stream from the tourism highly depends on a number of routes included in a tourist guide so the task is to find out a set of routes conforming the rules of a tourist guide with a maximum number of routes included.

The first line contains three integer numbers $ n,m,k $ $ (1

The first line of the output should contain $ c $ — the number of routes in a tourist guide. The following $ c $ lines should contain one tourist route each. Every route should be printed in a form of " $ t $ $ v_{1} $ $ v_{2} $ ... $ v_{t+1} $ ", where $ t $ is a number of roads in a route and $ v_{1},v_{2},...,v_{t+1} $ — cities listed in the order they are visited on the route. If there are multiple answers print any of them.