Triple Peaks

The Cordillera Oriental is a mountain range in the Andes that stretches across Bolivia. It consists of a sequence of $N$ mountain peaks, numbered from $0$ to $N - 1$. The height of peak $i$ ($0 \leq i < N$) is $H[i]$, which is an integer between $1$ and $N - 1$, inclusive.

For any two peaks $i$ and $j$ where $0 \leq i < j < N$, the distance between them is defined as $d(i, j) = j - i$.

According to ancient Inca legends, a triple of peaks is mythical if it has the following special property: the heights of the three peaks match their pairwise distances ignoring the order.

Formally, a triple of indices $(i, j, k)$ is mythical if

• $0 \leq i < j < k < N$, and
• the heights $(H[i], H[j], H[k])$ match the pairwise distances $(d(i,j), d(i,k), d(j,k))$ ignoring the order. For example, for indices $0, 1, 2$ the pairwise distances are $(1, 2, 1)$, so the heights $(H[0],H[1],H[2]) = (1,1,2)$, $(H[0],H[1],H[2]) = (1,2,1)$, and $(H[0],H[1],H[2]) = (2,1,1)$ all match them, but the heights $(H[0], H[1], H[2])=(1,2,2)$ do not match them.

This problem consists of two parts, with each subtask associated with either Part I or Part II. You may solve the subtasks in any order. In particular, you are not required to complete all of Part I before attempting Part II.