$\underline{\text { Kanel-Belov A.Y. }}$

There is one red and $k(k>1)$ blue cells, as well as a deck of $2 n$ cards numbered from 1 to $2 n$. Initially, the entire deck lies in a random order in the red cell. From any cell, you can take the top card and move it either to an empty cell or on top of a card with a number that is one greater. For what largest $n$ can the entire deck be moved to one of the blue cells using such operations?