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문제

There are $M$ boxes and $N$ balls. The balls are numbered $1$ through $N$, and the weight of the ball $i$ is $w_i$. You are also given a sequence $a_1, a_2, \ldots, a_K$. Each $a_j$ is an integer satisfying $1 \le a_j \le N$.

Initially, all the boxes are empty. For each $j = 1, 2, \ldots, K$ in this order, you have to perform the following operation:

  • If one of the boxes contains the ball $a_j$, you do nothing. There is no cost for this operation.
  • Otherwise, you choose one of the boxes and put the ball $a_j$ into the chosen box. However, if the chosen box already contains another ball, you should take that ball out of the box. The cost for this operation is $w_{a_j}$ (the cost doesn't depend on the box nor the ball you take out of the box).

Compute the minimum possible total cost of operations.

입력

The first line contains three integers $M$, $N$ and $K$ ($1 \le M \le 10$, $1 \le N, K \le 10^4$).

The $i$-th of the next $N$ lines contains an integer $w_i$ ($1 \le w_i \le 10^4$).

The $j$-th of the next $K$ lines contains an integer $a_j$ ($1 \le a_j \le N$).

출력

Print the minimum total cost.

예제 입력 1

3 3 6
10
20
30
1
2
3
1
2
3

예제 출력 1

60

예제 입력 2

2 3 6
10
20
30
1
2
3
1
2
3

예제 출력 2

80