Peter and Basil play the following game on a horizontal table 1×2019. Initially Peter chooses n positive integers and writes them on a board. After that Basil puts a coin in one of the cells. Then at each move, Peter announces a number s among the numbers written on the board, and Basil needs to shift the coin by s cells, if it is possible: either to the left, or to the right, by his decision. In case it is not possible to shift the coin by s cells neither to the left, nor to the right, the coin stays in the current cell. Find the least n such that Peter can play so that the coin will visit all the cells, regardless of the way Basil plays. Combinatorial gamescombinatorics