Maximal Rectangle in a Binary Matrix

You are given a binary matrix where each element is either 0 or 1. Your task is to find the area of the largest rectangle containing only 1's. A rectangle is defined by consecutive rows and columns and its area is given by \(\text{area} = \text{height} \times \text{width}\).

The matrix is provided as input with its dimensions, and you must output the maximum rectangular area formed solely by 1's.

For example, consider the matrix:

1 0 1 0 0
1 0 1 1 1
1 1 1 1 1
1 0 0 1 0

The maximal rectangle of 1's has an area of 6.

inputFormat

The input is read from standard input (stdin) and is formatted as follows:

• The first line contains an integer T, the number of test cases.
• For each test case, the first line contains two integers n and m representing the number of rows and columns of the matrix.
• Then follow n lines, each containing m space-separated integers (either 0 or 1) representing the matrix.

If n is 0, the matrix is empty and the answer is 0.

outputFormat

For each test case, output a single line with one integer representing the maximum area of a rectangle formed only by 1's. The output should be written to standard output (stdout).

## sample

2
4 5
1 0 1 0 0
1 0 1 1 1
1 1 1 1 1
1 0 0 1 0
2 2
1 1
1 1

6
4

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