A financial services company is uploading

documents to a compliance system for analysis.

They use a chunking mechanism as below.

Each document is divided into equal sized

packets.

Documents are then divided and uploaded in

"chunks" of packets. A chunk is defined as a

contiguous collection of $2^n$ packets, where $n$ is

any integer $0.$

After the document is divided into chunks,

randomly selected chunks are uploaded until the

entire document is completely uploaded.

There is one document that is partially uploaded,

described in uploadedChunks. Determine the

minimum number of chunks that are yet to be

uploaded.

Example

totalPackets $=5$

$n=2$ number of chunks already uploaded

uploadedChunks $=\left[\begin{array}{cc}1& 2\end{array}\right]$

The document has $5$ packets and $1$ chunk of $2^1=$

$2$ packets $[1,2]$ is already uploaded.

The remaining $3$ packets are uploaded in

$2$ chunks. The length of chunk $1$ is $2^1=2,$ packets

$3,4,$ and the length of chunk$2$ is $2^0=1$ packet

$[5].$