27052번 - Bale Figures 다국어

문제

Cows like to build shapes out of hay bales. Each new shape is constructed from N (1 ≤ N ≤ 25,000) 1 x 1 x 1 cubic bales.

Bale 1 lies on the floor. After placing it, each successive bale from 2 through N is attached to the shape by placing the new bale in the proper relative position to one of the bales already placed. For instance, imagine the following figure:

• Bale 1 - on the floor
• Bale 2 - RIGHT Bale 1 (to Bale 1's right)
• Bale 3 - FRONT Bale 2 (in front of Bale 2)
• Bale 4 - FRONT Bale 3

This results in an (inverted) L-shape:

 +--+--+ 
 1-> / / /| <-2 
 +--+--+ +
 | / /|/ 
 ++--+ + 
 / /|/ <-3 
 +--+ + 
 | |/ <-4 
 +--+ 

Adding another bale:

• Bale 5 - OVER Bale 1

adds height to the shape:

 +--+ 
 / /| 
 +--+ +--+ 
 5-> | |/ /| <-2 
 +--+--+ +
 1-> | / /|/ 
 ++--+ + 
 / /|/ <-3 
 +--+ + 
 | |/ <-4 
 +--+ 

But adding another directive:

• Bale 6 - BACK Bale 4

results in an invalid shape, since bales 3 and 6 would overlap.

Given N bales and placements described as above, output the exposed surface area of the solid figure if the shape is valid. A face is considered exposed if it is not touched by any face of any other bale and does not touch the floor (i.e., is not the bottom of a cube on the floor). Output -1 if the shape is invalid. No bale will be placed farther than 25 bale-widths from the first bale. No bale will be placed below the floor level.

입력

• Line 1: A single integer, N
• Lines 2..N: These lines describe the placement of bales 2..N in the form "j X". Line 2 describes bale 2; line 3 describes bale 3; and so on. The letter "X" is one of: "L" (left), "R" (right), "F" (front), "B" (back), "O" (over), or "U" (under). The bales can be glued and require no underlying support if extended over an empty space.

출력

• Line 1: The exposed surface area of the resulting solid. If the solid is invalid, output "-1".

제한

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