Pawn Chess

After winning the Candidates Tournament, Suzumo is intensively training for his upcoming match against Magus Cartesian. In order to improve his calculation skills, Suzumo invented a new game, which he named PawnChess. PawnChess is a two-player game played on a row of $N$ cells. Its rules are as follows: - Initially, some pawns are placed in some cells; each pawn is either black or white. There m