Sequences with no wells

A sequence of numbers has a well if it contains three consecutive numbers such that that the endpoints add up more than twice the one in the middle.

Formally, $(x_1, x_2 , \ldots , x_n)$ has a well if it exists at least an $i$ with $1 \leq i < n - 1$ such that $x_i + x_{i+2} > 2\cdot x_{i+1}$ .

Write a program that, given an integer $n \geq 1$ , writes all sequences with no well that can be obtained by reordering the sequence $(1, 2, \ldots , n)$ .

Input

The input consists of an integer $n \geq 1$ .

Output

Write all sequences with no well that can be obtained by reordering the sequence $(1, 2, \ldots, n)$ . You can write the sequences in any order.

Problem information

Author: Albert Oliveras

Generation: 2026-01-25T15:58:06.529Z