P7178 [COCI 2014/2015 #4] SABOR

In a faraway land, there are $n$ members of parliament. They are having a heated debate about a new amendment to the national referendum act. From Monday to Friday, all members happily come to work and argue all day long. A hardworking journalist takes photos at the workplace every workday each week during the heated debates. In each photo, she captures a pair of members staring angrily at each other. The five photos have been forwarded to you for a full analysis. In fact, each member belongs to one of two political parties. Let us denote the two parties by the letters `A` and `B`. Your task is to determine which party each member belongs to. You must ensure that each member quarrels with at most **two distinct** members of their own party.

The first line contains an integer $n$, the number of members of parliament. The members are numbered from $1$ to $n$. The next five lines describe the photos taken from Monday to Friday. Each of the five lines contains a list of pairs of members who are quarrelling (staring angrily at each other) in that day's photo. The first number on each line is $p$, meaning there are $p$ quarrels, followed by $p$ pairs of integers in the form `k l`, indicating that member $k$ and member $l$ are quarrelling. Before each pair of integers, there are **two spaces**.

Output a single line: a string of length $n$ consisting only of the characters `A` and `B`. The $i$-th character indicates which party the $i$-th member belongs to in a partition that satisfies the given condition. Since the solution is not unique, output **any** valid one.

#### Constraints - For $30\%$ of the testdata, $1 \le n \le 15$. - For $100\%$ of the testdata, $1 \le n \le 2 \times 10^5$. For every valid $p$, $1 \le p \le \dfrac{n}{2}$. #### Notes **Translated from [COCI2014-2015 CONTEST #4](https://hsin.hr/coci/archive/2014_2015/contest4_tasks.pdf) _T5 SABOR_.** Thanks to @[shenyouran](https://www.luogu.com.cn/user/137367) for providing the SPJ. Translated by ChatGPT 5