#P1820B. JoJo's Incredible Adventures
JoJo's Incredible Adventures
Description
Did you think there was going to be a JoJo legend here? But no, that was me, Dio!
Given a binary string $s$ of length $n$, consisting of characters 0 and 1. Let's build a square table of size $n \times n$, consisting of 0 and 1 characters as follows.
In the first row of the table write the original string $s$. In the second row of the table write cyclic shift of the string $s$ by one to the right. In the third row of the table, write the cyclic shift of line $s$ by two to the right. And so on. Thus, the row with number $k$ will contain a cyclic shift of string $s$ by $k$ to the right. The rows are numbered from $0$ to $n - 1$ top-to-bottom.
In the resulting table we need to find the rectangle consisting only of ones that has the largest area.
We call a rectangle the set of all cells $(i, j)$ in the table, such that $x_1 \le i \le x_2$ and $y_1 \le j \le y_2$ for some integers $0 \le x_1 \le x_2 < n$ and $0 \le y_1 \le y_2 < n$.
Recall that the cyclic shift of string $s$ by $k$ to the right is the string $s_{n-k+1} \ldots s_n s_1 s_2 \ldots s_{n-k}$. For example, the cyclic shift of the string "01011" by $0$ to the right is the string itself "01011", its cyclic shift by $3$ to the right is the string "01101".
Each test consists of multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 2 \cdot 10^4$) — the number of test cases. The description of test cases follows.
The first and the only line of each test case contains a single binary string $s$ ($1 \le \lvert s \rvert \le 2 \cdot 10^5$), consisting of characters 0 and 1.
It is guaranteed that the sum of string lengths $|s|$ over all test cases does not exceed $2 \cdot 10^5$.
For each test case, output a single integer — the maximum area of a rectangle consisting only of ones. If there is no such rectangle, output $0$.
Input
Each test consists of multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 2 \cdot 10^4$) — the number of test cases. The description of test cases follows.
The first and the only line of each test case contains a single binary string $s$ ($1 \le \lvert s \rvert \le 2 \cdot 10^5$), consisting of characters 0 and 1.
It is guaranteed that the sum of string lengths $|s|$ over all test cases does not exceed $2 \cdot 10^5$.
Output
For each test case, output a single integer — the maximum area of a rectangle consisting only of ones. If there is no such rectangle, output $0$.
5
0
1
101
011110
101010
0
1
2
6
1
Note
In the first test case, there is a table $1 \times 1$ consisting of a single character 0, so there are no rectangles consisting of ones, and the answer is $0$.
In the second test case, there is a table $1 \times 1$, consisting of a single character 1, so the answer is $1$.
In the third test case, there is a table:
| 1 | 0 | 1 |
| 1 | 1 | 0 |
| 0 | 1 | 1 |
In the fourth test case, there is a table:
| 0 | 1 | 1 | 1 | 1 | 0 |
| 0 | 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 1 | 1 |
| 1 | 1 | 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 1 | 0 | 0 |
In the fifth test case, there is a table:
| 1 | 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 0 | 1 | 0 | 1 |
| 1 | 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 0 | 1 | 0 | 1 |
| 1 | 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 0 | 1 | 0 | 1 |
Rectangles with maximum area are shown in bold.