OME 2023 Problem 5

We have a row of 203 cells. Initially the leftmost cell contains 203 tokens, and the rest are empty. On each move we can do one of the following: 1)Take one token, and move it to an adjacent cell (left or right). 2)Take exactly 20 tokens from the same cell, and move them all to an adjacent cell (all left or all right). After 2023 moves each cell contains one token. Prove that there exists a token that moved left at least nine times.