Floods

Author: munch

Poseidon is playing a game on a 69 \times 420 grid. At the start of the game, he floods k squares. Now, every second after the start of the game, if a cell is adjacent (doesn’t include diagonally adjacent cells) to at least 2 flooded cells, it becomes flooded. If a cell is flooded, it stays flooded. The game ends when no more cells can be flooded. What’s the minimum value of k such that we can flood all cells?