Need help with a GameTheory question from textbook

Consider the following three-player normal-form game. Player 1 chooses r e R+, player 2 chooses y e R+ while player 3 chooses 2 6 R+. Payoffs are given by ul(r, y, z) = 2x2 - ry, u2(x, y, 2) = V12(rty + 2) - y, us(r, y, 2) = 22 -ryzz. Solve for all (pure and mixed strategy) Nash equilibria. Hint: Calculate first the best-response correspondences for players 1 and 3 for every mixed strategy of the other players. Deduct from these that players 1 and 3 are going to play pure strategies in every Nash equilibrium, before calculating the best response correspondence of player 2 (against pure strategies only). In the end, you should arrive at a unique Nash equilibrium in pure strategies