Flappy Bird

Chef is playing a noob version of the game Flappy Bird with the following rules: - The bird starts at a height $H$ at $x = 0$. - There are $N$ obstacles (numbered $1$ through $N$). For each valid $i$, the $i$-th obstacle is at a position $x_i$ and it has a height $h_i$. - For each integer $i$ ($0 \le i \lt x_N$), Chef has the option to click once when the bird is at $x = i$. Let's denote the bird'