Minimalist Flooring

Algebra Level 5

b+c+da+a+c+db+a+b+dc+a+b+cd\large{\left \lfloor{\frac{b+c+d}{a}} \right \rfloor+ \left \lfloor{\frac{a+c+d}{b}} \right \rfloor+\left \lfloor{\frac{a+b+d}{c}} \right \rfloor+\left \lfloor{\frac{a+b+c}{d}} \right \rfloor}

For positive real numbers a,b,ca,b,c and dd, find the smallest possible value of the above expression.

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