Haven't you ever thought that an ordinary flat keyboard is boring, and you can come up with something more interesting?

A little boy named Kevin came up with a keyboard with $n$ unusual keys. Each key $i$ initially contains a sequence of letters: $L_{i, 1}, L_{i, 2}, \ldots, L_{i, |L_{i}|}$. Some letters in this sequence can be equal. Each letter is one of the first $e$ lowercase English letters. 

Every time key $i$ is pressed, the first letter of its sequence is typed and immediately moved to the end of the sequence. Thus, the first time key $i$ is pressed, letter $L_{i, 1}$ is typed, and the sequence becomes $L_{i, 2}, \ldots, L_{i, |L_{i}|}, L_{i, 1}$. The second time key $i$ is pressed, letter $L_{i, 2}$ is typed, and the sequence becomes $L_{i, 3}, \ldots, L_{i, |L_{i}|}, L_{i, 1}, L_{i, 2}$, and so on.

For example, suppose that key $1$ contains the sequence `\t{a}', `\t{b}', `\t{a}', and key $2$ contains the sequence `\t{c}',~`\t{d}'. Then, if you press keys $2, 1, 2, 2, 1, 1, 1, 2$ in this order, the string ``\t{cadcbaad}'' will be typed.

Help Kevin understand how useful his keyboard is, and find the shortest possible string consisting of the first $e$ lowercase English letters that cannot be typed with such a keyboard from the given initial state.