Long Inequality problem for $a, b, c $ positive real numbers $$ \left( a+\frac{1}{b} -1\right) \left( b+\frac{1}{c} - 1\right) +\left( b+\frac{1}{c} -1\right) \left( c+\frac{1}{a} -1\right) +\left( c+\frac{1}{a} -1\right) \left( a+\frac{1}{b} -1\right) \geq 3$$
How we can prove the inequality   above.  Actually it take long time to prove it but I couldn't complete.  How we prove it? . Thanks for help 

Hint:
$a,b,c$ are positive real numbers.
So,$a+\frac 1b>0$
So,$a+\frac 1b-1>-1$.
Similarly all the values are  greater than $-1$.
