Diverse Substrings

1000ms

262144K

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 $$$2$$$.

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 $$$s$$$.

Sample Input:

7
1
7
2
77
4
1010
5
01100
6
399996
5
23456
18
789987887987998798

Sample Output:

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.

Informação

Provedor Codeforces

Código CF1748B