Minimalist Flooring

Algebra Level 5

\[\large{\left \lfloor{\frac{b+c+d}{a}} \right \rfloor+ \left \lfloor{\frac{a+c+d}{b}} \right \rfloor+\left \lfloor{\frac{a+b+d}{c}} \right \rfloor+\left \lfloor{\frac{a+b+c}{d}} \right \rfloor}\]

For positive real numbers \(a,b,c\) and \(d\), find the smallest possible value of the above expression.