If \(\pi(n)\) denotes product of all binomial coefficients in \(\left(1+ x\right)^n\), then the ratio of \(\pi(2002)\) to \(\pi(2001)\) can be expressed as

###### Image Credit: Wikimedia Pascal Triangle by Dohduhdah

\[\dfrac{2002^{m}}{n!},\]

where \(m\) and \(n\) are positive integers. Fin the minimum value of \(m+n\).

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