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No.1292 Flipping Triangle

レベル : / AI推定難易度 : 1100 / 実行時間制限 : 1ケース 2.000秒 / メモリ制限 : 512 MB / 標準ジャッジ問題
タグ : （AC するまで非表示） / 解いたユーザー数 139
作問者 : 沙耶花 / テスター : SSRS
お気に入りにしたユーザー ProblemId : 3944 / 自分の提出
問題文最終更新日: 2020-11-20 21:08:12
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Problem Statement

There is an equilateral triangle of area 1 on a plane. Let us call its 3 sides side a, side b, and side c.

You will perform an operation $|S|$ times.
The $i$-th operation is described as follows, using the $i$-th character $s_i$ of the string $S$ given as input.

  • Reflect the triangle across side $s_i$.

Then, you
decide to paint every region where the triangle was located at any of the following moments: before performing the operations, immediately after the 1st operation, immediately after the 2nd operation, ..., immediately after the $|S|$-th operation.
That is, the regions occupied by the triangle at those moments get painted.

Find the area of the painted part.
(It can be shown that the answer is an integer. Output it as an integer value.)

Input

$S$

  • $1 \le |S| \le 2 \times 10^5$
  • Each character in $S$ is one of a, b, c

Output

Output the answer.
Print a newline at the end.

Sample

Sample 1
Input
abcc
Output
4

Sample 2
Input
cbacbbab
Output
8

Sample 3
Input
a
Output
2

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