The variables traverse, independently from each other, the set of positive real values. What are the values which the expression takes?
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The variables $a,b,c,d,$ traverse, independently from each other, the set of positive real values. What are the values which the expression $$S= \frac{a}{a+b+d} + \frac{b}{a+b+c} + \frac{c}{b+c+d} + \frac{d}{a+c+d}$$ takes?
Source: Međunarodna matematička olimpijada, shortlist 1974
Školjka 
traverse, independently from each other, the set of positive real values. What are the values which the expression 
takes?