The sequence \(a_1,a_2,a_3,\ldots\) satisfies \[ a_{n+2}=\dfrac{2}{a_{n+1}}+a_n , \quad n=1,2,3,\ldots.\]

with initial values \(a_1=1, a_2=2\).

Find the value of \(a_{100}\times a_{101}\).

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