FewestStrokes

Often, I find myself trying to repeat a certain character a great number of times in a primitive editor. For example, on many occasions I have had to make 50 periods. To type in a single character 50 times is very tedious, so I usually do something like type in the character 5 times, then copy those 5 occurrences of the character, and paste 5 characters at a time until I have 50. This might not be the best way to get 50 though, so in this problem, your task is to determine the optimal way to get a certain number of characters. You may use only the following keys:

1. The character to be repeated, which will be represented by a period ('.') in this problem.
2. The arrow keys, which allow you to move the cursor left or right. These will be represented by 'L' and 'R', respectively.
3. The home and end keys, which move to the beginning and end of the string of characters entered so far, respectively. These will be represented by 'H' and 'E', respectively.
4. The shift key which, when used in conjunction with the arrow keys or the home and end keys, allows you to select characters. We will represent depressing the shift key by 'D', and releasing it by 'U'. However, we will not count pressing or releasing the shift key as a keystroke, since that can be done without much added trouble.
5. The key combinations Ctrl-C and Ctrl-V, which allow you to copy and paste text, respectively. These will simply be represented by 'C' and 'V', respectively, and only count as a single keystroke each.
6. The backspace key allows you to delete one character immediately before (to the left of) the cursor, each time it is pressed. This will be represented by 'B'.

To select text using the shift key, you move the cursor to one end of the region to be selected, which we will call position pos₁ (indicating that there are pos₁ characters to the left of the cursor). You then hold down the shift key, and move the cursor to the other end of the region you want to select, at position pos₂. The text between the pos₁ and pos₂ is now selected, and, once the shift key is released, abs(pos₂-pos₁) characters may be copied using Ctrl-C (Ctrl-C has no other effect, other than to copy the selected text). If any key other than home, end, left, or right is pressed while the shift key is depressed, that key has no effect. If any key other than Ctrl-C is pressed while text is selected, the text is first deselected, the cursor position is set to pos₂ and then the operation defined by that key is performed. So, if you select text, and then press backspace, the text is first deselected, the cursor position is set to pos₂, and then a single character is deleted (or there is no effect if the cursor is at the beginning of the line). When pasting text, the most recently copied number of characters (abs(pos₂-pos₁)) are inserted at the cursor position, and the cursor moves to the end of the pasted text.

For example, the sequence "....DHUCVVB" will perform the following:
First, we type 4 characters. Next we depress the shift key, and press the home key, and release the shift key, selecting all four characters. We now copy the four characters and paste twice, so there are 12 characters and the cursor is between the 8th and 9th characters. Finally, we press backspace to delete one of them, leaving us with 11 characters in 9 keystrokes (remember not to count 'U' and 'D').

Your task is to compute and return the minimum number of keystrokes required to create exactly n occurrences of a character. Thus, in the above example, we got 11 characters in 9 keystrokes, and since it turns out that there is no way to get 11 characters in less than 9 keystrokes, we would return 9 if n were 11.