Bessie, always wishing to optimize her life, has realized that she really enjoys visiting $F$ $(1 \le F \le P)$ favorite pastures $F_{i}$ of the $P$ $(1 \le P \le 500; 1 \le F_{i} \le P)$ total pastures (conveniently numbered $1,\ldots,P$) that compose Farmer John's holdings.

Bessie knows that she can navigate the $C$ $(1 \le C \le 8,000)$ bidirectional cowpaths (conveniently numbered $1,\ldots,C$) that connect various pastures to travel to any pasture on the entire farm. Associated with each path $P_{i}$ is a time $T_{i}$ $(1 \le T_{i} \le 892)$ to traverse that path (in either direction) and two path endpoints $a_{i}$ and $b_{i}$ $(1 \le a_{i} \le P; 1 \le b_{i} \le P)$.

Bessie wants to find the number of the best pasture to sleep in so that when she awakes, the average time to travel to any of her $F$ favorite pastures is minimized.

By way of example, consider a farm laid out as the map below shows, where *'d pasture numbers are favorites. The bracketed numbers are times to traverse the cowpaths.

            1*--[4]--2--[2]--3
                     |       |
                    [3]     [4]
                     |       |
                     4--[3]--5--[1]---6---[6]---7--[7]--8*
                     |       |        |         |
                    [3]     [2]      [1]       [3]
                     |       |        |         |
                    13*      9--[3]--10*--[1]--11*--[3]--12*

The following table shows distances for potential 'best place' of pastures 4, 5, 6, 7, 9, 10, 11, and 12:

                       * * * * * * Favorites * * * * * *
 Potential      Pasture Pasture Pasture Pasture Pasture Pasture     Average
Best Pasture       1       8      10      11      12      13        Distance
------------      --      --      --      --      --      --      -----------
    4              7      16       5       6       9       3      46/6 = 7.67
    5             10      13       2       3       6       6      40/6 = 6.67
    6             11      12       1       2       5       7      38/6 = 6.33
    7             16       7       4       3       6      12      48/6 = 8.00
    9             12      14       3       4       7       8      48/6 = 8.00
   10             12      11       0       1       4       8      36/6 = 6.00 ** BEST
   11             13      10       1       0       3       9      36/6 = 6.00
   12             16      13       4       3       0      12      48/6 = 8.00

Thus, presuming these choices were the best ones (a program would have to check all of them somehow), the best place to sleep is pasture 10.

Input

• Line 1: Three space-separated integers: $P$, $F$, and $C$
• Lines $2,\ldots,F+1$: Line $i+2$ contains a single integer: $F_{i}$
• Lines $F+2,\ldots,C+F+1$: Line $i$+$F+1$ describes cowpath $i$ with three space-separated integers: $a_{i}$, $b_{i}$, and $T_{i}$

Output

• Line 1: A single line with a single integer that is the best pasture in which to sleep. If more than one pasture is best, choose the smallest one.

Examples

Input 1

13 6 15
11
13
10
12
8
1
2 4 3
7 11 3
10 11 1
4 13 3
9 10 3
2 3 2
3 5 4
5 9 2
6 7 6
5 6 1
1 2 4
4 5 3
11 12 3
6 10 1
7 8 7

Output 1

10

As the problem statement

As the problem statement.

Problem credits: Rob Kolstad, 2009