Straddle Gamma Across Price Movement

You are long a straddle (long call + long put at the same strike $K$ and expiry $T$) under Black-Scholes assumptions. Explain how the portfolio gamma varies as the underlying spot price $S$ moves. Specifically: 1. What is the gamma at-the-money ($S = K$)? 2. How does gamma change as $S$ moves away from $K$ in either direction? 3. How does time to expiry affect the gamma profile?