A16272. Largest Subsequence

Given is a string $s$ of length $n$ . In one operation you can select the lexicographically largest $^\dagger$ subsequence of string $s$ and cyclic shift it to the right $^\ddagger$ .

Your task is to calculate the minimum number of operations it would take for $s$ to become sorted, or report that it never reaches a sorted state.

$^\dagger$ A string $a$ is lexicographically smaller than a string $b$ if and only if one of the following holds:

- $a$ is a prefix of $b$ , but $a \ne b$ ;
- In the first position where $a$ and $b$ differ, the string $a$ has a letter that appears earlier in the alphabet than the corresponding letter in $b$ .

$^\ddagger$ By cyclic shifting the string $t_1t_2\ldots t_m$ to the right, we get the string $t_mt_1\ldots t_{m-1}$ .

Each test consists of multiple test cases. The first line contains a single integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ) — the length of the string $s$ .

The second line of each test case contains a single string $s$ of length $n$ , consisting of lowercase English letters.

It is guaranteed that sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ .

For each test case, output a single integer — the minimum number of operations required to make $s$ sorted, or $-1$ if it's impossible.

In the first test case, the string $s$ is already sorted, so we need no operations.

In the second test case, doing one operation, we will select cb and cyclic shift it. The string $s$ is now abc which is sorted.

In the third test case, $s$ cannot be sorted.

In the fourth test case we will perform the following operations:

- The lexicographically largest subsequence is zca. Then $s$ becomes abzc.
- The lexicographically largest subsequence is zc. Then $s$ becomes abcz. The string becomes sorted.

Thus, we need $2$ operations.