K-sorting

Sorting involves arranging a given array of numbers (or other objects) in either ascending or descending order. There are numerous variations of this task, many of which have highly efficient algorithms. A key parameter of these algorithms is the number of swaps needed to sort the array elements.

In this problem, we explore a variant called $k$-sorting. In $k$-sorting, you can perform a $k$-swap, which allows you to swap the values of two array elements whose indices differ by exactly $k$. For instance, consider the array [$6$, $10$, $4$, $1$, $2$] with $k=3$. This array can be sorted in ascending order with two operations: after the first swap, the array becomes [$1$, $10$, $4$, $6$, $2$], and after the second swap, it becomes [$1$, $2$, $4$, $6$, $10$].

Given an array of integers $a_1,a_2,\dots ,a_n$, your task is to find the minimum number of $k$-swaps required to sort this array in non-decreasing order.

Input

The first line contains an integer $n$ ($1\le n\le 300$). The second line contains $n$ integers $a_1,a_2,\dots ,a_n$ ($1\le a_i\le 10^9$ for all $i$ from $1$ to $n$). The third line contains an integer $k$ ($1\le k\le n-1$).

Output

If the array can be sorted in non-decreasing order using the described operations, output the minimum number of $k$-swaps needed. If it is not possible to sort the array this way, output $-1$.

Examples