Let a parabola with focus \( (5, 5) \) touches the two lines : \[\displaystyle{ L }_{ 1 }:\quad y=\quad x+1, \\ { L }_{ 2 }:\quad y=-x+1. \]

the equation of the parabola be : \[\displaystyle\left| \frac { ax-by+c }{ \sqrt { d } } \right| \quad =\quad \sqrt { { (x-e) }^{ 2 }+{ (y-e) }^{ 2 } }. \]

Find Value of \(a+b+c+d+e\)

**Details and assumptions**

- \(a ,b ,c,d,e\) are all
**Positive**integers, '\(d\)' is square free integer. And Don't count '\(e\)' twice .

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