B. Maximum Substringtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputA binary string is a string consisting only of the characters 0 and 1. You are given a binary string s.For some non-empty substring^\dagger t of string s containing x characters 0 and y characters 1, define its cost as:  x \cdot y, if x > 0 and y > 0;  x^2, if x > 0 and y = 0;  y^2, if x = 0 and y > 0. Given a binary string s of length n, find the maximum cost across all its non-empty substrings.^\dagger 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.InputEach test consists of multiple test cases. The first line contains a single integer t (1 \leq t \leq 10^5) — the number of test cases. The description of 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 binary string s of length n.It is guaranteed that the sum of n over all test cases does not exceed 2 \cdot 10^5.OutputFor each test case, print a single integer — the maximum cost across all substrings.ExampleInput
6511100711001106011110710010104100010Output
9
12
16
12
9
1
NoteIn the first test case, we can take a substring 111. It contains 3 characters 1 and 0 characters 0. So a = 3, b = 0 and its cost is 3^2 = 9.In the second test case, we can take the whole string. It contains 4 characters 1 and 3 characters 0. So a = 4, b = 3 and its cost is 4 \cdot 3 = 12.In the third test case, we can can take a substring 1111 and its cost is 4^2 = 16.In the fourth test case, we can take the whole string and cost is 4 \cdot 3 = 12.In the fifth test case, we can take a substring 000 and its cost is 3 \cdot 3 = 9.In the sixth test case, we can only take the substring 0 and its cost is 1 \cdot 1 = 1.
6511100711001106011110710010104100010
9 12 16 12 9 1 
['brute force', 'greedy', 'implementation', '*800']