Obtuse Angle Decomposition
Given a natural number n.
Your task is to divide the set {2, 3, 4, ..., 3n+1} into n triples such that each triple forms the sides of a non-degenerate obtuse triangle.
Input
The input consists of a single line containing a natural number n (1 ≤ n ≤ 30000).
Output
Output exactly n lines. On the i-th line, write three numbers a_i, b_i, c_i separated by spaces, representing the sides of the i-th triangle. If there are multiple solutions, you may output any of them. It is guaranteed that a solution always exists. Specifically, the output (a_1, b_1, c_1), ..., (a_n, b_n, c_n) will be correct if and only if the set {a_1, b_1, c_1, ..., a_n, b_n, c_n} is identical to {2, 3, 4, ..., 3n+1} and for each i from 1 to n, the numbers a_i, b_i, c_i form a non-degenerate obtuse triangle. The order of numbers within each triple and the order of the triples themselves can be arbitrary.