Pretty cool Fibonacci

Let \({ F }_{ n }\) be the \(n\)th Fibonacci number. Find the first four digits of the number of digits of \({ F }_{ p }\), where \(p={ 10 }^{ 12 }\).

Details: \({ F }_{ n }={ F }_{ n-1 }+{ F }_{ n-2 }\) and \({ F }_{ 0 }=0 \) and \({ F }_{ 1 }=1\).

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