Problem

Source: 239 MO 2021 (8-9).7

Tags: combinatorics, catalan



Given is a grid with $2$ rows and $120$ columns, such that each cell has a number from the set $1, 2, ..., 120$. It is known that in each column, the upper number in it is smaller than the lower number, and in each row, the numbers are in non-strict increasing order from left to right. Prove that the number of these tables is multiple of $239$.