Largest Rectangle in a Histogram

A histogram has bars of width 1 with the given heights. Find the area of the largest rectangle that lies entirely within the bars. A monotonic stack gives an O(n) solution.

Implement largest_rectangle(heights).

Input

heights: Bar heights from left to right.

Output

Return the largest area.

Restrições

0 ≤ length ≤ 200,000; 0 ≤ height ≤ 1,000,000,000

Exemplos

Entrada:
heights = [2, 1, 5, 6, 2, 3]

Saída esperada:
expected = 10

Entrada:
std::vector<long long> heights = {2, 1, 5, 6, 2, 3};

Saída esperada:
long long expected = 10;

Entrada:
long[] heights = new long[] {2, 1, 5, 6, 2, 3};

Saída esperada:
long expected = 10;

Entrada:
heights = [4]

Saída esperada:
expected = 4

Entrada:
std::vector<long long> heights = {4};

Saída esperada:
long long expected = 4;

Entrada:
long[] heights = new long[] {4};

Saída esperada:
long expected = 4;

Referências

Este desafio foi adaptado para o CodeUtility. Siga o enunciado e as restrições acima.

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