Pia Atelier: Alchemist of the Mystery Competition

The game Pia Atelier: Alchemist of the Mystery Competition tells the growth story of Pia, a poor alchemist. The competition is the central part. Pia earns a living only when alchemy produces high quality goods and wins prize money. The story is long and is omitted here. This task asks you to check the competition logic.

You place $3$ distinct materials in order into a $5 \times 5$ grid furnace and build a bomb of the highest possible quality. The competition supplies at most $10$ candidate materials. You choose $3$ of them, fix an order, and place them into the furnace.

Each furnace cell holds a quality number and an element color. At the start every cell has quality $0$ and white color. Each material has $4 \times 4$ shape, and cell $(i, j)$ of a material holds two values.

1. Efficacy: an integer $x_{i,j}$ from $-9$ to $9$ that is added to the quality of one furnace cell.
2. Element: a color $c_{i,j}$ that can change the element of one furnace cell, one of red R, blue B, green G, yellow Y, and white W.

A material never sticks out of the $5 \times 5$ grid. Rotation in steps of $90$ degrees is allowed, and tilted placement is not allowed. When a material is placed, the furnace changes as follows.

1. A cell outside the material does not change.

2. A cell under the material changes as follows.

   • Quality grows by the efficacy of the material. A negative sum becomes $0$, and a sum above $9$ becomes $9$.
   • Color stays the same when the material element is white, and otherwise becomes the material element color.

The bomb is complete only after all $3$ materials are placed. Let $R$, $B$, $G$, and $Y$ be the quality sums over cells colored red, blue, green, and yellow in the finished furnace. The bomb quality is $7R + 5B + 3G + 2Y$.

Given the candidate materials, choose and place them to maximize the bomb quality.

The first line holds a natural number $n$, the count of candidate materials ($3 \le n \le 10$).

The next lines hold the $n$ materials in order. Each material uses $8$ lines. The first $4$ lines hold efficacy: $4$ integers separated by spaces on each line. The next $4$ lines hold elements: $4$ characters separated by spaces on each line. Each character is one of R, B, G, Y, W.

Print the maximum bomb quality on the first line.

The placement proceeds as follows.

0. Initial furnace.

1. Place the second material with its top left corner at row $1$, column $1$, rotated once counterclockwise.

2. Place the third material with its top left corner at row $2$, column $2$, without rotation.

3. Place the first material with its top left corner at row $2$, column $1$, rotated once counterclockwise.

The sums are $R = 69$, $B = 21$, $G = 4$, and $Y = 17$, so the final quality is $634$.