Assume function genPerm$($n: number$)$: number$[]$ creates a random permutation of the numbers $0..$ n$-1.$

Given the code:

function rotate$($a: number$[])$: number$[]\{$

if $($a$.$length $>0)$ a$.$push$($a$.$shift$()$ as number$)$; $//$ removes first element, shifts others by one to front, adds element at end

return a;

$\}$

function genInput$($n: number$)$: number$[][]\{$

const m: number$[][]=[]$;

let a $=$ genPerm$($n$)$; $//$ generates random permutation

for $($let i $=$ n; $--$i $>=0$;$)$ m$.$push$($rotate$($a$))$;

return m;

$\}$

const m $=$ genInput$(5)$;

If we now sum each column of m$,$ what is the largest sum?