MathDB

There is a table with

n > 2

cells in the first row,

n-1

cells in the second row is a cell,

n-2

in the third row,

\ldots

1

cell in the

n

-th row. The cells are arranged as shown below.
https://i.ibb.co/0Z1CR0c/UMO24-8-2.png
In each cell of the top row Petryk writes a number from

1

n

, so that each number is written exactly once. For each other cell, if the cells directly above it contains numbers

a, b

, it contains number

|a-b|

. What is the largest number that can be written in a single cell of the bottom row?
Proposed by Bogdan Rublov

Problem Statement