P5143 Climber

After finishing GDOI, HKE went to climb a mountain with his "shenben" friends.

He marked $N$ points on a topographic map, where each point $P_i$ has coordinates $(x_i, y_i, z_i)$. Among all points, the height values $z$ are pairwise distinct. HKE plans to climb from the lowest point to the highest point, and his climbing satisfies the following conditions: (1) He visits every point he marked. (2) Starting from the second point, the height $z$ of each visited point is higher than that of the previous point. (3) HKE can fly. The distance he travels from a point $P_i$ to $P_j$ is the Euclidean distance between the two points, i.e., $\sqrt{(X_i-X_j)^2+(Y_i-Y_j)^2+(Z_i-Z_j)^2}$. Now, HKE wants you to compute the total distance of his climb.

The first line contains an integer $N$ indicating the number of points on the map. Each of the next $N$ lines contains three integers $x_i, y_i, z_i$, representing the coordinates of the $i$-th point.

Output a real number representing the total distance HKE needs to climb (rounded to three decimal places).

For 100% of the testdata, $1\leq N\leq 50000$, and the answer is within the range of a double. Translated by ChatGPT 5