Platforms#798
In some old video games, one may encounter the following scenario. A hero must jump across a sequence of platforms suspended in the air, moving from one edge of the screen to the other. Jumping from one platform to its immediate neighbor costs the hero |y_2 - y_1| units of energy, where y_1 and y_2 are the heights of the respective platforms. The hero also has a special move: a super jump that allows him to skip exactly one platform (i.e., jump from platform to platform i+2). Such a super jump costs 3 \cdot |y_3 - y_1| units of energy, where y_1 and y_3 are the heights of the starting and landing platforms.
Given the heights of all platforms from left to right, find the minimum amount of energy required to reach the -th (last) platform from the -st (first) platform. Also, print the exact sequence of platforms (by their indices) that the hero must visit to achieve this minimum.
The first line contains the number of platforms (2 \le n \le 10^5). The second line contains integers, the heights of the platforms. The absolute value of each height does not exceed .
Print the minimum required amount of energy to travel from the first to the last platform. In the second line, print the number of platforms in the sequence (including the first and the last). In the third line, print the sequence of platform indices in order.
Example 1
Example 2