Maximum Rectangular Area in a Histogram

You are given one or more histograms. Each histogram is represented on a single line as a sequence of nonnegative integers separated by spaces. In each line, the histogram values are followed by a trailing 0, which serves as a marker and should be ignored when processing the histogram. The input terminates with a line that contains only a single 0.

Your task is to compute, for each histogram, the maximum rectangular area under the histogram. For a given contiguous group of bars, the area is computed as \(\text{Area} = \text{height} \times \text{width}\), where the height is the minimum height among the chosen bars and the width is the number of bars. Output the maximum area you can obtain for each histogram on a separate line.

inputFormat

The input is read from standard input (stdin). It consists of several lines. Each line (except the last) represents a histogram: a sequence of space-separated nonnegative integers ending with 0. The final input line is a single 0 which marks the termination of the input.

For example, the following input describes two histograms:

2 1 5 6 2 3 0
4 2 0
0

outputFormat

For each histogram (except the termination line), output a single line containing the maximum rectangular area that can be found within that histogram.

For the sample input above, the output would be:

10
4

## sample

2 1 5 6 2 3 0
4 2 0
0

10
4

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