The developers at Amazon are working on optimbing their database query ores. There are nhosi servers, where the throughput of the $\backslash ($ f$^\{\backslash$text $\{$th $\}\}\backslash )$ hast server is given by hast whroughputg?

These host servers are grouped inso cluvers of side three. The throughput of a cluster, denoted as cluster throughout is defined as the median of the host, throughoul value: bet the three servers in the cluster. Each host server can be part of ar most one custer, and some servers moy remain urused.

Then tocal system throughput, called systam, throsghout, is che sum of the throughputs of al the cluciers formed. The tank is to find the maxmum fossible syacme throughpu:

Note The medan of a clusere of three host swevers is the throughput of the and server when the three throughputs are ported in ether nysending or Gestending proder.

Example

$\backslash [$

n$-5$

$\backslash ]$

hast througriout $\backslash (=[2,3,4,4]\backslash )$

The macomut number of chasters that can bs formand is $1,$ and twa haw severs will remal$-$ unused.

Frus. the system troughipurfor al chastera will be $4.$

Runction Description

Daturns

Constraints

$-\backslash (14\backslash$mathrm$\{$se$\}\backslash$times $2=10^\{\backslash$circ$\}\backslash )$