def matrix_chain_order(p):
    n = len(p) - 1
    m = [[0] * n for _ in range(n)]
    s = [[0] * n for _ in range(n)]
    for L in range(2, n + 1):
        for i in range(n - L + 1):
            j = i + L - 1
            m[i][j] = 10**18
            for k in range(i, j):
                q = m[i][k] + m[k + 1][j] + p[i] * p[k + 1] * p[j + 1]
                if q < m[i][j]:
                    m[i][j] = q
                    s[i][j] = k
    return m, s


def build_parenthesization(s, i, j, names):
    if i == j:
        return names[i]
    k = s[i][j]
    return (
        "("
        + build_parenthesization(s, i, k, names)
        + build_parenthesization(s, k + 1, j, names)
        + ")"
    )


if __name__ == "__main__":
    p = [30, 35, 15, 5, 10, 20, 25]
    names = ["A", "B", "C", "D", "E", "F"][: len(p) - 1]
    m, s = matrix_chain_order(p)
    expr = build_parenthesization(s, 0, len(p) - 2, names)
    print(m[0][len(p) - 2])
    print(expr)