Chef and Modulo Game

Chef is playing a game with two of his friends. In this game, each player chooses an integer between $1$ and $P$ inclusive. Let's denote the integers chosen by Chef, friend 1 and friend 2 by $i$, $j$ and $k$ respectively; then, Chef's score is $$(((N\,\mathrm{mod}\,i)\,\mathrm{mod}\,j)\,\mathrm{mod}\,k)\,\mathrm{mod}\,N\,.$$ Chef wants to obtain the maximum possible score. Let's d