CF88B.Keyboard

Vasya learns to type. He has an unusual keyboard at his disposal: it is rectangular and it has n rows of keys containing m keys in each row. Besides, the keys are of two types. Some of the keys have lowercase Latin letters on them and some of the keys work like the "Shift" key on standard keyboards, that is, they make lowercase letters uppercase.

Vasya can press one or two keys with one hand. However, he can only press two keys if the Euclidean distance between the centers of the keys does not exceed x. The keys are considered as squares with a side equal to 1. There are no empty spaces between neighbouring keys.

Vasya is a very lazy boy, that's why he tries to type with one hand as he eats chips with his other one. However, it is possible that some symbol can't be typed with one hand only, because the distance between it and the closest "Shift" key is strictly larger than x. In this case he will have to use his other hand. Having typed the symbol, Vasya returns other hand back to the chips.

You are given Vasya's keyboard and the text. Count the minimum number of times Vasya will have to use the other hand.

瓦西娅正在学习打字。他使用一种特殊的键盘：该键盘呈矩形，共有 $n$ 行，每行包含 $m$ 个按键。此外，按键分为两类：一部分按键上印有小写拉丁字母，另一部分按键则起到类似标准键盘上“Shift”键的作用，即将小写字母转换为大写。

瓦西娅可用一只手同时按下一个或两个按键。但只有当所按两个按键中心之间的欧几里得距离不超过 $x$ 时，才允许同时按下两个键。每个按键被视为边长为 $1$ 的正方形，相邻按键之间无空隙。

瓦西娅非常懒，因此他试图仅用一只手打字（另一只手则用来吃薯片）。然而，某些字符可能无法单手输入，因为该字符所在按键与最近的“Shift”键之间的距离严格大于 $x$。此时，他必须用另一只手来按“Shift”键。在输入该字符后，瓦西娅会立即将另一只手放回薯片上。

现给出瓦西娅的键盘布局及待输入的文本，请计算瓦西娅最少需要使用另一只手的次数。

The first line contains three integers n, m, x (1 ≤ n, m ≤ 30, 1 ≤ x ≤ 50).

Next n lines contain descriptions of all the keyboard keys. Each line contains the descriptions of exactly m keys, without spaces. The letter keys are marked with the corresponding lowercase letters. The "Shift" keys are marked with the "S" symbol.

Then follow the length of the text q (1 ≤ q ≤ 5·105). The last line contains the text T, which consists of q symbols, which are uppercase and lowercase Latin letters.

第一行包含三个整数 $n$、$m$、$x$（$1 \leq n, m \leq 30$，$1 \leq x \leq 50$）。

接下来的 $n$ 行描述键盘上的所有按键。每行恰好包含 $m$ 个按键的描述，中间无空格。字母键用对应的小写字母标记；“Shift” 键用字符 “S” 标记。

随后一行给出文本长度 $q$（$1 \leq q \leq 5\cdot10^5$）。最后一行包含文本 $T$，其由 $q$ 个字符组成，每个字符均为大写或小写的拉丁字母。

If Vasya can type the text, then print the minimum number of times he will have to use his other hand. Otherwise, print "-1" (without the quotes).

如果瓦西娅能够输入该文本，则输出他最少需要使用另一只手的次数；否则，输出“-1”（不带引号）。

In the first sample the symbol "A" is impossible to print as there's no "Shift" key on the keyboard.

In the second sample the symbol "e" is impossible to print as there's no such key on the keyboard.

In the fourth sample the symbols "T", "G" are impossible to print with one hand. The other letters that are on the keyboard can be printed. Those symbols come up in the text twice, thus, the answer is 2.

在第一个样例中，无法输入符号 “A”，因为键盘上没有 “Shift” 键。

在第二个样例中，无法输入符号 “e”，因为键盘上没有该按键。

在第四个样例中，符号 “T” 和 “G” 无法用单手输入。键盘上的其余字母均可输入。这些符号在文本中总共出现了两次，因此答案为 2。