Binary Code

Ben has just learned about binary prefix codes. A binary code is a set of $n$ distinct nonempty code words $s_i$, each made of 0s and 1s. A code is a prefix code if for every $i \ne j$, $s_i$ is not a prefix of $s_j$ and $s_j$ is not a prefix of $s_i$. A word $x$ is a prefix of a word $w$ if there is a word $y$, possibly empty, with $xy = w$. For example, $x = 11$ is a prefix of $w = 110$, and $x = 0100$ is a prefix of $w = 0100$.

Ben found a paper with $n$ lines of binary code on it. The paper is old, so some of the characters cannot be read. Each word contains at most one unreadable character.

Decide whether these $n$ lines can represent a binary prefix code. That is, decide whether Ben can replace every unreadable character with 0 or 1 so that the whole set becomes a prefix code.

The first line contains the number of code words $n$ ($1 \le n \le 5 \times 10^5$).

Each of the next $n$ lines contains one code word record. A record is nonempty and consists of the characters 0, 1 and ?, where ? stands for an unreadable character. Every record contains at most one ?.

The total length of the records does not exceed $5 \times 10^5$.

Print YES on the first line if every ? can be replaced by 0 or 1 so that the words form a prefix code, and NO otherwise. Do not print the completed code words.