There is an infinite chessboard. The chessboard is split in two by a horizontal line that extends indefinitely. Above the dividing line, the cells of the chessboard should stay empty. Below you may place as many pawns as you want in any approach you want. To transfer a pawn you carry out the next transfer: a pawn jumps over an adjoining pawn to an empty cell. The pawn that was stepped over is eaten and disappears from the chessboard whereas the one which jumps can solely achieve this horizontally or vertically however not diagonally. Evidently, there can’t be two pawns per cell. Also, a pawn can not transfer until it eats one other pawn.

For instance, if there’s a pawn in cell B1 and a pawn in cell C1, then the pawn in B1 can leap to the proper into the cell D1 by consuming the pawn in C1, which is faraway from the board. Similarly, the pawn in C1 can eat the pawn in B1 by leaping into cell A1.

The objective is to get a pawn as excessive as potential above the horizontal dividing line.
What is the best line above the horizontal dividing line that may be reached?