Problem Statement

There are $N towns numbered 1, \dots, N$, and $M roads numbered 1, \dots, M$.
Every road is directed; road $i (1 \leq i \leq M)$ leads you from Town A_i to Town B_i. The length of road i is C_i.
You are given $a sequence E = (E_1, \dots, E_K)$ of length K consisting of integers between 1 and M. A way of traveling from town 1 to town N using roads is called a good path if:

• the sequence of the roads' numbers arranged in the order used in the path is a subsequence of E.

Note that a subsequence of a sequence is a sequence obtained by removing 0 or more elements from the original sequence and concatenating the remaining elements without changing the order.
Find the minimum sum of the lengths of the roads used in a good path.
If there is no good path, report that fact.

Input

The input is given from Standard Input in the following format:
N M K
A_1 B_1 C_1
$\vdots$
A_M B_M C_M
$E_1 \ldots E_K$

Output

Find the minimum sum of the lengths of the roads used in a good path.
If there is no good path, print -1.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq M, K \leq 2 \times 10^5$
• $1 \leq A_i, B_i \leq N, A_i \neq B_i$ $, (1 \leq i \leq M)$
• $1 \leq C_i \leq 10^9$ $, (1 \leq i \leq M)$
• $1 \leq E_i \leq M$ $, (1 \leq i \leq K)$
• All values in the input are integers.

Sample Input 1

3 4 4
1 2 2
2 3 2
1 3 3
1 3 5
4 2 1 2

Sample Output 1

4

There are two possible good paths as follows:

• Using road 4. In this case, the sum of the length of the used road is 5.
• Using road 1 and 2 in this order. In this case, the sum of the lengths of the used roads is 2 + 2 = 4.

Therefore, the desired minimum value is 4.

Sample Input 2

3 2 3
1 2 1
2 3 1
2 1 1

Sample Output 2

-1

There is no good path.

Sample Input 3

4 4 5
3 2 2
1 3 5
2 4 7
3 4 10
2 4 1 4 3

Sample Output 3

14

见题面 Input 部分

见题面 Output 部分