Problem Statement

$N$ eggs are lined up in a row.

Each egg is painted in one of the colors represented by integers from $1$ to $M$, and the $i \: (1 \leq i \leq N)$-th egg from the left is painted in color $C_i$.

You may choose any egg and repaint it any number of times, and repainting an egg to color $j \: (1 \leq j \leq M)$ costs $A_j$.

Find the minimum cost required to make the colors of some $K$ consecutive eggs all the same.

Constraints

• $1 \leq K \leq N \leq 2 \times 10^{5}$
• $1 \leq M \leq 2 \times 10^{5}$
• $1 \leq C_i \leq M$
• $1 \leq A_j \leq 10^{9}$
• All input values are integers.

Input

The input is given from standard input in the following format.

$N$ $M$ $K$ 
$C_1$ $C_2$ ... $C_N$ 
$A_1$ $A_2$ ... $A_M$ 

Output

Output the answer to the problem on one line.

Sample

5 3 3
1 2 1 3 2
10 10 10

10

5 3 3
1 1 1 1 1
10 10 10

0