Your father once shared with you a thrilling story from his days as a spy during a family reunion. He had traveled around the world gathering critical information, and one of his favorite memories was from a mission that required him to infiltrate a secret organization.

On that mission, his objective was to retrieve a report hidden in the deepest vault of a heavily secured basement. To access the vault, he had to crack a keypad, which required a passcode composed of English letters. Although he didn't know the passcode, luck was on his side. While hiding in a nearby vent, he overheard the organization's boss entering the code. He couldn't see the keypad, but he could still hear the sounds of the keys being pressed.

The keypad worked like the multi-tap system found on old phones, where pressing a key multiple times cycles through the letters associated with that key. If, for example, the passcode was $$$cat$$$, the boss would have to press the $$$2$$$ key three times for $$$c$$$, pause, press $$$2$$$ again for $$$a$$$, pause, and then press $$$7$$$ once for $$$t$$$.

Figure B.1: Examples of the keypad

Typically, pressing a key more times than the number of characters it represents will cycle back to the first character. However, the boss was extremely cautious and never pressed a key too many times. For instance, he would never press the $$$2$$$ key four times to type the letter $$$a$$$.

Each key produced a distinct pitch, and your father, with his keen ear, could identify which buttons were pressed. He jotted down the tapping sequence in his notebook but didn't record the pauses. For instance, if the passcode was $$$cat$$$, he would have written down $$$22228$$$.

Later, he realized he could simply have slipped into the vault before the door shut completely. Using his stealth skills, he managed to enter the vault, retrieve the report, and escape the building without being detected.

A few days after the mission, curiosity got the better of him. He looked back at the tapping sequence he had noted and wondered about the passcode. Now you are also intrigued; what passcode could it possibly be ?