Score : $500$ points

问题陈述

有一个城镇，表示为一个二维网格，有 $H$ 行水平行和 $W$ 列垂直列。 一个字符 $a_{i,j}$ 描述了从顶部数第 $i$ 行和从左边数第 $j$ 列的正方形。在这里，$a_{i,j}$ 是以下之一：S，G，.，#，a，...，z。 # 表示一个不能进入的正方形，而 a，...，z 表示有传送门的正方形。

高桥最初在表示为 S 的正方形。在每一秒钟，他将进行以下移动之一：

• 移动到当前位置水平或垂直相邻的非 # 方块。
• 选择一个与当前位置相同字符的正方形，并传送到那个正方形。只有当他在一个表示为 a，...，或 z 的正方形时，他才能使用这个移动。

找出高桥从表示为 S 的正方形到达表示为 G 的正方形所需的最短时间。 如果目的地无法到达，请报告 -1。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

There is a town represented as a two-dimensional grid with $H$ horizontal rows and $W$ vertical columns.
A character $a_{i,j}$ describes the square at the $i$-th row from the top and $j$-th column from the left. Here, $a_{i,j}$ is one of the following: S , G , . , # , a, ..., and z.
# represents a square that cannot be entered, and a, ..., z represent squares with teleporters.

Takahashi is initially at the square represented as S. In each second, he will make one of the following moves:

• Go to a non-# square that is horizontally or vertically adjacent to his current position.
• Choose a square with the same character as that of his current position, and teleport to that square. He can only use this move when he is at a square represented as a, ..., or z.

Find the shortest time Takahashi needs to reach the square represented as G from the one represented as S.
If the destination is unreachable, report -1 instead.

Constraints

• $1 \le H, W \le 2000$
• $a_{i,j}$ is S, G, ., #, or a lowercase English letter.
• There is exactly one square represented as S and one square represented as G.

Input

Input is given from Standard Input in the following format:

$H$ $W$

$a_{1,1}\dots a_{1,W}$

$\vdots$

$a_{H,1}\dots a_{H,W}$

Output

Print the shortest time Takahashi needs to reach the square represented as G from the one represented as S.
If the destination is unreachable from the initial position, print -1 instead.

Sample Input 1

2 5
S.b.b
a.a.G

Sample Output 1

4

Let $(i, j)$ denote the square at the $i$-th row from the top and $j$-th column from the left.
Initially, Takahashi is at $(1, 1)$. One way to reach $(2, 5)$ in four seconds is:

• go from $(1, 1)$ to $(2, 1)$;
• teleport from $(2, 1)$ to $(2, 3)$, which is also an a square;
• go from $(2, 3)$ to $(2, 4)$;
• go from $(2, 4)$ to $(2, 5)$.

Sample Input 2

11 11
S##...#c...
...#d.#.#..
..........#
.#....#...#
#.....bc...
#.##......#
.......c..#
..#........
a..........
d..#...a...
.#........G

Sample Output 2

14

Sample Input 3

11 11
.#.#.e#a...
.b..##..#..
#....#.#..#
.#dd..#..#.
....#...#e.
c#.#a....#.
.....#..#.e
.#....#b.#.
.#...#..#..
......#c#G.
#..S...#...

Sample Output 3

-1