The equation of the parabola whose focus is \(\displaystyle \left( 1,-1 \right)\) and vertex is \(\displaystyle \left( 2,1 \right)\) can be written in the form \(\displaystyle a{ x }^{ 2 }+2hxy+{ by }^{ 2 }+2gx+2fy+c=0\).

Find the value of \(\displaystyle Z\), where \(\displaystyle Z=a+h+b+g+f+c\).

**Details And Assumption**

\(\displaystyle \gcd\left( \left| a \right|, \left| h \right|, \left| b \right|, \left| g \right|, \left| f \right|, \left| c \right| \right) =1\)

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