A15556 | Diverse Substrings

A non-empty digit string is diverse if the number of occurrences of each character in it doesn't exceed the number of distinct characters in it.

For example:

- string "7" is diverse because 7 appears in it $1$ time and the number of distinct characters in it is $1$ ;
- string "77" is not diverse because 7 appears in it $2$ times and the number of distinct characters in it is $1$ ;
- string "1010" is diverse because both 0 and 1 appear in it $2$ times and the number of distinct characters in it is $2$ ;
- string "6668" is not diverse because 6 appears in it $3$ times and the number of distinct characters in it is $2$ .

You are given a string $s$ of length $n$ , consisting of only digits $0$ to $9$ . Find how many of its $\frac{n(n+1)}{2}$ substrings are diverse.

A string $a$ is a substring of a string $b$ if $a$ can be obtained from $b$ by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end.

Note that if the same diverse string appears in $s$ multiple times, each occurrence should be counted independently. For example, there are two diverse substrings in "77" both equal to "7", so the answer for the string "77" is $2$ .

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

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

The second line of each test case contains a string $s$ of length $n$ . It is guaranteed that all characters of $s$ are digits from $0$ to $9$ .

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

For each test case print one integer — the number of diverse substrings of the given string $s$ .