Build `n` towers from 1 to `n`.\nHeight of the `i-th` tower, `a_i`, cannot be greater than `m_i` meters. (1 <= `a_i` <= `m_i`)\nThere cannot be integers `j` and `k` such that there exist `j` < `i` < `k` and `a_j` > `a_i` and `a_i` < `a_k`.\nGiven a list of `M`, return a list `A` so that the sum of all `a_i` is the maximum possible one.\n(Thus, the sequence of building heights can have at most a single peak, and no valley)\n\nExample 1:\n```\nInput: [1, 2, 3, 2, 1]\nOutput: [1, 2, 3, 2, 1]\nExplanation: Sum=9 with 3 as the peak\n```\n\nExample 2:\n```\nInput: [10, 6, 8]\nOutput: [10, 6, 6]\nExplanation: Sum=22 with 10 as the peak, other valid sequences with a lower sum can be [6, 6, 6] or [6, 6, 8]\n```\n\nExample 3:\n```\nInput: [7, 7, 1, 9, 1, 7, 7]\nOutput: [7, 7, 1, 1, 1, 1, 1] or [1, 1, 1, 1, 1, 7, 7]\nExplanation: Sum=19 with 7 as the peak, [1, 1, 1, 9, 1, 1, 1] is also valid but has sum of 15\n```\n\nI couldn\'t find a solution better than O(n^2). Thoughts?\n\n

Build n towers from 1 to n.\nHeight of the i-th tower, a_i, cannot be greater than m_i meters. (1 <= a_i <= m_i)\nThere cannot be integers j and k such that the