\[ \Large \frac{20102011}{2012} = a + \frac{1}{b + \frac{1}{c + \frac{1}{d + \frac{1}{e + \frac{1}{f + \frac 1g} } }}} \]

If \(a,b,c,d,e,f,g \) are positive integers that fulfill the equation above, find the value of \(a-b+c-d+e-f+g\).

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