Find and Replace
Contest: Codeforces Round 859 (Div. 4)
Difficulty rating: 800
Tags: greedy, implementation, strings

You are given a string $$$s$$$ consisting of lowercase Latin characters. In an operation, you can take a character and replace all occurrences of this character with $$$\texttt{0}$$$ or replace all occurrences of this character with $$$\texttt{1}$$$.

Is it possible to perform some number of moves so that the resulting string is an alternating binary string$$$^{\dagger}$$$?

For example, consider the string $$$\texttt{abacaba}$$$. You can perform the following moves:

- Replace $$$\texttt{a}$$$ with $$$\texttt{0}$$$. Now the string is $$$\color{red}{\texttt{0}}\texttt{b}\color{red}{\texttt{0}}\texttt{c}\color{red}{\texttt{0}}\texttt{b}\color{red}{\texttt{0}}$$$.
- Replace $$$\texttt{b}$$$ with $$$\texttt{1}$$$. Now the string is $$${\texttt{0}}\color{red}{\texttt{1}}{\texttt{0}}\texttt{c}{\texttt{0}}\color{red}{\texttt{1}}{\texttt{0}}$$$.
- Replace $$$\texttt{c}$$$ with $$$\texttt{1}$$$. Now the string is $$${\texttt{0}}{\texttt{1}}{\texttt{0}}\color{red}{\texttt{1}}{\texttt{0}}{\texttt{1}}{\texttt{0}}$$$. This is an alternating binary string.

$$$^{\dagger}$$$An alternating binary string is a string of $$$\texttt{0}$$$s and $$$\texttt{1}$$$s such that no two adjacent bits are equal. For example, $$$\texttt{01010101}$$$, $$$\texttt{101}$$$, $$$\texttt{1}$$$ are alternating binary strings, but $$$\texttt{0110}$$$, $$$\texttt{0a0a0}$$$, $$$\texttt{10100}$$$ are not.

Input format:
The input consists of multiple test cases. The first line contains an integer $$$t$$$ ($$$1 \leq t \leq 100$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer $$$n$$$ ($$$1 \leq n \leq 2000$$$) — the length of the string $$$s$$$.

The second line of each test case contains a string consisting of $$$n$$$ lowercase Latin characters — the string $$$s$$$.

Output format:
For each test case, output "YES" (without quotes) if you can make the string into an alternating binary string, and "NO" (without quotes) otherwise.

You can output the answer in any case (for example, the strings "yEs", "yes", "Yes" and "YES" will be recognized as a positive answer).

Constraints:
Time limit: 1.0 s
Memory limit: 256.0 MB

Note:
The first test case is explained in the statement.

In the second test case, the only possible binary strings you can make are $$$\texttt{00}$$$ and $$$\texttt{11}$$$, neither of which are alternating.

In the third test case, you can make $$$\texttt{1}$$$, which is an alternating binary string.

Example input:
8
7
abacaba
2
aa
1
y
4
bkpt
6
ninfia
6
banana
10
codeforces
8
testcase

Example output:
YES
NO
YES
YES
NO
YES
NO
NO

Editorial:
Let's solve a harder problem: given a string $$$s$$$ and a binary string $$$t$$$, can we make $$$s$$$ into $$$t$$$ using the find and replace operations?
We can simply iterate through each character of $$$s$$$ and see the bit it has turned to in $$$t$$$ (that is, $$$s_i \to t_i$$$ for each $$$i$$$). Keep track of each change, and see if there is some letter that needs to be turned into both $$$\texttt{0}$$$ and $$$\texttt{1}$$$. If there is some letter, it is impossible, since each operation requires changing all occurrences of a letter into the same bit. Otherwise, it is possible, and we can directly change each letter into the bit it needs to be. (See the implementation for a better understanding.)
Now for this problem, since there are only two alternating binary strings of length $$$n$$$ ($$$\texttt{01010...}$$$ and $$$\texttt{10101...}$$$), we can simply check both. (Actually, we only have to check one — do you see why?) The time complexity is $$$\mathcal{O}(n)$$$.