Multi-Tap Encoding

You are given a string s of English letters (either case) and spaces, containing at least one letter.

On a classic phone keypad, each digit from 2 to 9 carries a group of letters, and a letter is typed by pressing its digit repeatedly: once for the first letter of the group, twice for the second, and so on:

Return the encoding of s as a sequence of key presses, applying these rules:

• Spaces in s are ignored.
• Uppercase and lowercase letters are treated the same.
• Each letter is replaced by its key-press sequence from the table.
• If two consecutive letters (after ignoring spaces) use the same key, insert a single # between their encodings. Letters on different keys are concatenated directly.

The # separator makes the encoding unambiguous: without it, the encoding of "AB" would read 222, which is the encoding of "C".

Examples

Example 1

Input: s = "AB"
Output: "2#22"
Explanation: A and B share key 2, so their encodings 2 and 22 are separated by #.

Example 2

Input: s = "AD"
Output: "23"
Explanation: A (key 2) and D (key 3) use different keys, so no separator is needed.

Example 3

Input: s = "HEY EPIC"
Output: "4433999337444222"
Explanation: H → 44, E → 33, Y → 999, E → 33, P → 7, I → 444, C → 222. The space is ignored, and no two consecutive letters share a key, so the encodings are concatenated directly.