There is a directed graph with $N$ vertices and $M$ edges.  
The vertices are numbered $1, \dots, N$, and the $i$-th edge $(1 \leq i \leq M)$ goes from Vertex $A_i$ to Vertex $B_i$.

Initially, there are $X_i$ items on Vertex $i$ $(1 \leq i \leq N)$ that someone has lost. $K$ people will collect these items.

The $K$ people will travel in the graph one by one. Each person will do the following.

-   Start on Vertex $1$. Then, traverse an edge any finite number of times. For each vertex visited (including Vertex $1$), collect all items on it if they have not been collected yet.

Find the maximum total number of items that can be collected.

Input is given from Standard Input in the following format:

```
$N$ $M$ $K$
$A_1$ $B_1$
$\vdots$
$A_M$ $B_M$
$X_1$ $\ldots$ $X_N$
```

Print the answer.

-   $2 \leq N \leq 2 \times 10^5$
-   $1 \leq M \leq 2 \times 10^5$
-   $1 \leq K \leq 10$
-   $1 \leq A_i, B_i \leq N$
-   $A_i \neq B_i$
-   $A_i \neq A_j$ or $B_i \neq B_j$, if $i \neq j$.
-   $1 \leq X_i \leq 10^9$
-   All values in input are integers.

18

The two people can collect 18 items as follows.

• The first person goes 1→2→3→2 and collects the items on Vertices 1, 2, and 3.
• The second person goes 1→5 and collects the items on Vertex 5.

It is impossible to collect 19 or more items, so we should print 18.