def max_double_slice_sum(a: list[int]) -> int:
    size = len(a)
    if size < 3:
        return 0

    p1 = {1: 0}
    p2 = {size - 2: 0}

    for i in range(2, size - 1):
        p1[i] = max(0, p1[i - 1] + a[i - 1])
        p2[size - i - 1] = max(0, p2[size - i] + a[size - i])

    total = p1[1] + p2[1]
    for i in range(1, size - 1):
        total = max(total, p1[i] + p2[i])

    return total