Given an n x n integer matrix grid, return the minimum sum of a falling path with non$-$zero shifts.

A falling path with non$-$zero shifts is a choice of exactly one element from each row of grid such that no two elements chosen in adjacent rows are in the same column.

Input: grid $=[[1,2,3],[4,5,6],[7,8,9]]$

Output: $13$

Explanation:

The possible falling paths are:

$[1,5,9],[1,5,7],[1,6,7],[1,6,8],$

$[2,4,8],[2,4,9],[2,6,7],[2,6,8],$

$[3,4,8],[3,4,9],[3,5,7],[3,5,9]$

The falling path with the smallest sum is $[1,5,7],$ so the answer is $13.$

Example $2$:

Input: grid $=[[7]]$

Output: $7$

Constraints:

n $==$ grid.length $==$ grid$[$i$].$length

$1<=$ n $<=200$

$-99<=$ grid$[$i$][$j$]<=99$