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# [Solution] Diverse Substrings Codeforces Solution

B. Diverse Substrings
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $\frac{n\left(n+1\right)}{2}$ 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 $s$.

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.