Secret

The Greatest Secret Ever consists of n words, indexed by positive integers from 1 to n. The secret needs dividing between k Keepers (let's index them by positive integers from 1 to k), the i-th Keeper gets a non-empty set of words with numbers from the set U_i = (u_i, 1, u_i, 2, ..., u_i, |Ui|). Here and below we'll presuppose that the set elements are written in the increasing order.

We'll say that the secret is safe if the following conditions are hold:

• for any two indexes i, j (1 ≤ i < j ≤ k) the intersection of sets U_i and U_j is an empty set;
• the union of sets U₁, U₂, ..., U_k is set (1, 2, ..., n);
• in each set U_i, its elements u_i, 1, u_i, 2, ..., u_i, |Ui| do not form an arithmetic progression (in particular, |U_i| ≥ 3 should hold).

Let us remind you that the elements of set (u₁, u₂, ..., u_s) form an arithmetic progression if there is such number d, that for all i (1 ≤ i < s) fulfills u_i + d = u_i + 1. For example, the elements of sets (5), (1, 10) and (1, 5, 9) form arithmetic progressions and the elements of sets (1, 2, 4) and (3, 6, 8) don't.

Your task is to find any partition of the set of words into subsets U₁, U₂, ..., U_k so that the secret is safe. Otherwise indicate that there's no such partition.