There is an infinite chessboard. The chessboard is divided in two by a horizontal line that extends indefinitely. Above the dividing line, the cells of the chessboard must remain empty. Below you can place as many pawns as you like in any way you like. To move a pawn you perform the following move: a pawn jumps over an adjacent pawn to an empty cell. The pawn that was stepped over is eaten and disappears from the chessboard while the one that jumps can only do so horizontally or vertically but not diagonally. Evidently, there cannot be two pawns per cell. Also, a pawn cannot move unless it eats another pawn.
For example, if there is a pawn in cell B1 and a pawn in cell C1, then the pawn in B1 can jump to the right into the cell D1 by eating the pawn in C1, which is removed from the board. Similarly, the pawn in C1 can eat the pawn in B1 by jumping into cell A1.
The goal is to get a pawn as high as possible above the horizontal dividing line. What is the highest line above the horizontal dividing line that can be reached?