from collections import namedtuple
from collections import deque

Rect = namedtuple("Rect", ["cols", "rows"])


def sub_rectangles(rect):
    r = [Rect(i, j)
          for i in range(1, rect.cols + 1)
          for j in range(1, rect.rows + 1)]
    return r

def flat_fit(n_inner, n_outer):
    return n_outer - n_inner + 1

def count_fits(sub_rect, main_rect):
    row_fits = flat_fit(sub_rect.rows, main_rect.rows)
    col_fits = flat_fit(sub_rect.cols, main_rect.cols)
    return row_fits * col_fits


def count_sub_rectangles(rect):
    r = 0
    for sub_rect in sub_rectangles(rect):
        r += count_fits(sub_rect, rect)
    return r


def euler_085():
    limit = 2 * 10**6
    nearest = 0
    canditate_rects = deque([Rect(1, 1)])

    while canditate_rects:
        rect = canditate_rects.popleft()
        sub_count = count_sub_rectangles(rect)
        # print(rect, sub_count)

        if sub_count < limit and sub_count > nearest:
            nearest = sub_count

        if sub_count == 1999998:
            return rect.cols * rect.rows
        elif sub_count < limit:
            canditate_rects.append(Rect(rect.cols + 0, rect.rows + 1))
        else:
            canditate_rects.append(Rect(rect.cols + 1, 1))


if __name__ == "__main__":
    s = euler_085()
    print("e085.py: " + str(s))
    assert(s == 2772)