You are given:

• A stock has price 50.

• A market-maker writes put option P1 on the stock with price 1.53, delta -0.39, and gamma 0.072.

• The market-maker delta-gamma hedges the option with the stock and with another put option P2 having price 2.00, delta -0.31, and gamma 0.038. Find the number of shares of stock to buy to implement the hedge.