# Solution of;
# Project Euler Problem 538: Maximum quadrilaterals
# https://projecteuler.net/problem=538
# 
# Consider a positive integer sequence S = (s1, s2, . . . , sn). Let f(S) be 
# the perimeter of the maximum-area quadrilateral whose side lengths are 4 
# elements (si, sj, sk, sl) of S (all i, j, k, l distinct). If there are many 
# quadrilaterals with the same maximum area, then choose the one with the 
# largest perimeter. For example, if S = (8, 9, 14, 9, 27), then we can take 
# the elements (9, 14, 9, 27) and form an isosceles trapezium with parallel 
# side lengths 14 and 27 and both leg lengths 9. The area of this 
# quadrilateral is 127. 611470879. . . It can be shown that this is the 
# largest area for any quadrilateral that can be formed using side lengths 
# from S. Therefore, f(S) = 9 + 14 + 9 + 27 = 59. Let un = 2B(3n) + 3B(2n) + 
# B(n+1), where B(k) is the number of 1 bits of k in base 2. For example, B(6) 
# = 2, B(10) = 2 and B(15) = 4, and u5 = 24 + 32 + 2 = 27. Also, let Un be the 
# sequence (u1, u2, . . . , un). For example, U10 = (8, 9, 14, 9, 27, 16, 36, 
# 9, 27, 28). It can be shown that f(U5) = 59, f(U10) = 118, f(U150) = 3223. 
# It can also be shown that ∑ f(Un) = 234761 for 4 ≤ n ≤ 150. Find ∑ f(Un) for 
# 4 ≤ n ≤ 3 000 000.
# 
# by lcsm29 http://github.com/lcsm29/project-euler
import timed


def dummy(n):
    pass


if __name__ == '__main__':
    n = 1000
    i = 10000
    prob_id = 538
    timed.caller(dummy, n, i, prob_id)
