KöMaL 2016 B4781

The rows and the columns of an $n \times n$ chessboard are numbered 1 to $n$ , and a coin is placed on each field. The following game is played: A coin showing tails is selected. If it is in row $k$ and column $m$ , then every coin with row number at least $k$ and column number at least $m$ is turned over. This procedure is repeated. What is the least number $L(n)$ for which it is possible to achieve in at most $L(n)$ steps that all coins on the board show heads, whatever be the initial distribution of heads and tails?