Diverse Substrings
Description
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 $s$.
Input
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 $10^5$.
Output
For each test case print one integer — the number of diverse substrings of the given string $s$.
7
1
7
2
77
4
1010
5
01100
6
399996
5
23456
18
789987887987998798
1
2
10
12
10
15
106
Note
In the first test case, the diverse substring is "7".
In the second test case, the only diverse substring is "7", which appears twice, so the answer is $2$.
In the third test case, the diverse substrings are "0" ($2$ times), "01", "010", "1" ($2$ times), "10" ($2$ times), "101" and "1010".
In the fourth test case, the diverse substrings are "0" ($3$ times), "01", "011", "0110", "1" ($2$ times), "10", "100", "110" and "1100".
In the fifth test case, the diverse substrings are "3", "39", "399", "6", "9" ($4$ times), "96" and "996".
In the sixth test case, all $15$ non-empty substrings of "23456" are diverse.