Queen Game

Queen game is played on a chessboard with $R$ rows and $C$ columns. Rows are numbered from $1$ to $R$, and columns from $1$ to $C$. The top-left square is at row $1$ and column $1$. Two players play the game. Initially, there are $N$ queens placed on various squares of the chessboard. On each turn, a player picks a queen and moves it either vertically upwards, horizontally to the left, or diagonally up-left. The queen must always remain on the board. When a queen reaches square $(1,1)$, it is removed from the board. The player who makes the last move wins. Each square is large enough to hold any number of queens. Players alternate turns. You are given the size of the chessboard and the initial positions of the $N$ queens. Assuming both players play optimally, determine who will win the game.