The government of Cuckooland decided that each province of such a huge country should have its own flag. A famous painter Cuckooshkin was told to create all flags. It is known that Cuckooshkin uses only n different colors in his paintings. According to the government's plan, every two flags of provinces should have at least one common color, which will symbolize integrity of the country. On the other hand, the painter wants to make these flags as varicoloured as possible, so he doesn't want any colour to occur in three or more flags. What is the maximal number of flags Cuckooshkin can create without breaking neither his own nor government's requirements?
The first line contains the only integer n (3 ≤ n ≤ 1000), the number of colors the painter can use. The colors are numbered 1 to n.
In the first line output the integer k, the maximal number of flags the painter can create. Each of the next k lines should contain description of the next flag: first, the number of colors used in it and then the numbers of these colors. All integers in this line should be separated by single space. In case there are many correct answers, you can output any of them.
2 1 2
2 1 3
2 2 3
Problem Author: Igor Chevdar
Problem Source: Ural SU Contest. Petrozavodsk Winter Session, February 2009