Determine all possible values of S=aa+b+d+ba+b+c+cb+c+d+da+c+dS = \frac{a}{a+b+d} + \frac{b}{a+b+c} + \frac{c}{b+c+d} + \frac{d}{a+c+d}S=a+b+da+a+b+cb+b+c+dc+a+c+dd where aaa, bbb, ccc, ddd are arbitrary positive numbers.