You are planning a hike in the Peneda-Gerês National Park in the north of Portugal. The park takes its name from two of its highest peaks: Peneda (1340 m) and Gerês (1545 m). For this problem, the park is modelled as an infinite plane, where each position ((x, y)), with (x, y) being integers, has a specific altitude. The altitudes are defined by an (n \times n) matrix (h), which repeats periodically across the plane. Specifically, for any integers (a, b) and (0 \leq x, y < n), the altitude at ((x + an, y + bn)) is (hxy). When you are at position ((x, y)), you can move to any of the four adjacent positions: ((x, y+1)), ((x+1, y)), ((x, y-1)), or ((x-1, y)). The time required to move between two adjacent positions is (1 + \lvert \text{alt}_1 - \text{alt}_2 \rvert), where (\text{alt}_1) and (\text{alt}_2) are the altitudes of the current and destination positions, respectively. Initially, your position is ((0, 0)). Compute the number of distinct positions you can reach within (10^{20}) seconds. Your answer will be considered correct if its relative error is less than (10^{-6}). The first line contains an integer (n) ((2\le n\le 20))—the size of the matrix describing the altitudes. The following (n) lines contain (n) integers each. The ((j+1))-th number on the ((i+1))-th of these lines is (hij) ((0\le hij \le 1545))—the altitude of the position ((i, j)). Print the number of distinct positions you can reach within (10^{20}) seconds. Your answer will be considered correct if its relative error is less than (10^{-6}). In the first sample , every position of the Peneda-Gerês National Park has an altitude of (3). Therefore, the time required to move between two adjacent positions is always equal to (1) second. In this case, one can show that a position ((x, y)) is reachable within (10^{20}) seconds if and only if $$$|x|