Problem Statement

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.

Constraints

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

Input

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

Output

Print the answer.