	\begin{problem}{Protoss Defense}{\textsl{standard input}}{\textsl{standard output}}{1 second}{512 mebibytes}{}


        General High Templar wants to relieve The World of disgusting invaders.
        His right hand, military commander Tryt o'Kill is ready to perform the
        plan of the destruction of the enemies. Plan is as simple as brilliant...
        To locate and to annihilate all enemy military targets!

        So, the military commander Tryt o'Kill has been ordered to destroy enemy
        creatures. He has decided to provide missile attack on the enemy
        targets. But this task is not so simple... These targets are heavily
        defended by $K$ different layers of defense. The first layer consists
        of \textit{forward air defense sites} (FADS), the second layer consists of
        \textit{band surface to air missiles} (BSAM), the third layer consists of
        \textit{airborne interceptors} (AI), the other layers consists of different
        kinds of \textit{terminal surface to air missiles} (TSAM); a  $(K+1)$-th layer
        contains the military targets themselves. Of course, some targets
        might not be defended while some others might have all defense
        layers.

        Tryt o'Kill is good at math and he has denoted by $S$ the set of all defense sites and
        by $T$ the set of the enemy targets. A defense site might also provide protection to other defense sites
        in higher-numbered layers. Some defense sites might protect neither targets nor other defense sites.
        Commander also denoted by $D_i$ the set of defense sites that protect the target or defense site $i\in T\cup S$.
        Let $L_i$ denotes the layer's number of  $i\in T\cup S$. Of course,
        $$
            \forall\, i \in T \cup S \quad \forall\, j \in D_i \quad
            \Rightarrow \quad L_i > L_j.
        $$
        Based on his past experience, Tryt o'Kill feels that while it might be possible for missiles to pass
        through all the defenses and reach the military targets, the probability of such a ``leakage''{} is quite small.
        Instead, he believes that to destroy a target, he must first destroy all the defense sites that protect it.
        Therefore, he must destroy defense sites as well as targets. Destroying the $i$-th target or defense site has a
        certain military benefit and some loss. So, Commander knows the so called ``cost-effectiveness''{} $c_i$ of destroying the  $i$-th target
        or defense site. The military commander wants to identify a set of targets and defense sites with the largest
        possible total ``cost-effectiveness.''{} It might be possible that providing missile attack is unreasonable and it
        would be better to choose nothing.

        \InputFile

        Let's suppose that all targets and defense sites are numbered from $1$  to $n$, where  $n=|S \cup T|$.
        In the first line of the input file integer numbers  $n$, $m$ and $K$ are written. The second line contains $c_i$
        $(i=1,2,\ldots,n)$; moreover, $-10^6\leq c_i \leq 10^6$.
        The third line is made up of $L_j$ $(j=1,2,\ldots,n)$ divided by space ($1 \leq L_j \leq K+1$).
    Next $m$ lines consist of pairs of numbers $i$ and $j$;
    each pair $(i,j)$ means that $j \in D_i$  and  $L_i>L_j$.
        Look at the example below to get more evident information. Keep in mind that $0 < n \leq 200$,  $0 \leq K < 200$,  $0 \leq m \leq 40\,000$.

        \OutputFile

    Write the largest possible total ``cost-effectiveness''{} of chosen targets or defense sites in the first line of the output file.
    Write on the second line the number of targets of defense sites to destroy. On the third line write numbers of chosen targets or defense sites
    in ascending order. If there are several solutions, output any one of them.

	\Examples

        \begin{example}
	\exmp{5 4 2        
        5 -3 -4 3 2  
        3 2 2 1 1    
        2 4
        1 3
        3 4
        3 5}{6
	 4
	 1 3 4 5}%
	\exmp{
        5 4 2        
        1 2 1 -5 -5  
        3 2 2 1 1    
        2 4
        1 3
	3 4
        3 5}{0
	0}%	
        \end{example}

    \end{problem}
