def merge_at(s, i):
    s[i] += s[i+1]
    del s[i+1]
    return s[i]

def merge_force_collapse(s):
    cost = 0
    while len(s) > 1:
        n = len(s) - 2
        if n > 0 and s[n-1] < s[n+1]:
            n -= 1
        cost += merge_at(s, n)
    return cost

def sort(runs, merge_collapse):
    stack = []
    maxstack = 0
    cost = 0
    for x in runs:
        stack.append(x)
        maxstack = max(maxstack, len(stack))
        cost += merge_collapse(stack)
    cost += merge_force_collapse(stack)
    return cost, maxstack

def timsort(s):
    cost = 0
    while len(s) > 1:
        n = len(s) - 2
        if ((n > 0 and s[n-1] <= s[n] + s[n+1]) or
            (n > 1 and s[n-2] <= s[n-1] + s[n])):
            if s[n-1] < s[n+1]:
                n -= 1
            cost += merge_at(s, n)
        elif s[n] <= s[n+1]:
            cost += merge_at(s, n)
        else:
            break
    return cost

def twomerge(s):
    cost = 0
    while len(s) > 1:
        n = len(s) - 2
        if s[n] < 2 * s[n+1]:
            if n > 0 and s[n-1] < s[n+1]:
                n -= 1
            cost += merge_at(s, n)
        else:
            break
    if len(s) > 1:
        assert s[-2] >= 2 * s[-1]
        if len(s) > 2:
            assert s[-3] >= 2 * s[-2]
    return cost

if 1:
    from random import random, randrange

    print("all the same") # identical stats
    runs = [32] * 1000
    print(sort(runs, timsort))
    print(sort(runs, twomerge))

    print("ascending")  # timsort a little better
    runs = range(1, 2000)
    print(sort(runs, timsort))
    print(sort(runs, twomerge))

    print("descending") # twomerge significantly better
    print(sort(reversed(runs), timsort))
    print(sort(reversed(runs), twomerge))

    # "Random" run-length distributions are largely irrelevant, since on
    # randomly ordered input the actual sort is most likely to _force_
    # (via local binary insertion sorts) all runs to length `minrun`.
    # Nevertheless ... there's no clear overall winner in this
    # particular made-up distribution.  On some runs timsort "wins" in
    # the end, on others twomerge, but the total costs are typically
    # within 2% of each other.
    print("randomized trials")
    totals = [0, 0]
    for trial in range(20):
        runs = []
        for i in range(1000):
            switch = random()
            if switch < 0.80:
                x = randrange(1, 100)
            else:
                x = randrange(1000, 10000)
            runs.append(x)
        for i, which in enumerate([timsort, twomerge]):
            cost, depth = sort(runs, which)
            print(f"{which.__name__:8s}", cost, depth)
            totals[i] += cost
        print("sofar", totals, "timsort excess",
              f"{(totals[0] - totals[1]) / totals[1]:.2%}")