import math

binaryLen = lambda n: math.floor(math.log2(n)) + 1

def findNextMx(mx, ar , exclude_list):
	'''Find the next max of same bin len as mx.'''
    logmx = binaryLen(mx)
    nextmx = float('-inf')
    for n in ar:
        if n not in exclude_list and n > nextmx:
            nextmx = n
    if binaryLen(nextmx) != logmx:
        mx = nextmx
        return findNextMx(nextmx, ar, exclude_list + [nextmx])
    return mx, nextmx

def maxAnd(ar):
    mx = max(ar)
    mx, nextmx = findNextMx(mx, ar , [mx])
    return mx & nextmx

def maxOR(ar):
    mx = max(ar)
    mx, nextmx = findNextMx(mx, ar , [mx])
    return mx | nextmx

def sumMaxAndOr(ar):
    mx = max(ar)
    mx, nextmx = findNextMx(mx, ar , [mx])
    return (mx & nextmx) +  (mx | nextmx)