Storing binary trees

Binary trees can be stored in an array as follows:

Indexing of the array starts at \(1\) instead of \(0\). For an array \(P\), the root is stored at \(P[1]\). For a node stored at \(P[i]\), the left child, if any, is stored in \(P[2i]\) and the right child, if any, in \(P[2i+1]\).

What should be the minimum size of array \(P\) to be able to store any binary tree of \(n\) vertices?

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