Problem:
Score : 400 points

Problem Statement

There are N towns in the State of Atcoder, connected by M bidirectional roads.

The i-th road connects Town A_i and B_i and has a length of C_i.

Joisino is visiting R towns in the state, r_1,r_2,..,r_R (not necessarily in this order).

She will fly to the first town she visits, and fly back from the last town she visits, but for the rest of the trip she will have to travel by road.

If she visits the towns in the order that minimizes the distance traveled by road, what will that distance be?

Constraints

2≤N≤200

1≤M≤N×(N-1)/2

2≤R≤min(8,N) (min(8,N) is the smaller of 8 and N.)

r_i≠r_j (i≠j)

1≤A_i,B_i≤N, A_i≠B_i

(A_i,B_i)≠(A_j,B_j),(A_i,B_i)≠(B_j,A_j) (i≠j)

1≤C_i≤100000

Every town can be reached from every town by road.

All input values are integers.

Input

Input is given from Standard Input in the following format:

N M R
r_1 ... r_R
A_1 B_1 C_1
:
A_M B_M C_M

Output

Print the distance traveled by road if Joisino visits the towns in the order that minimizes it.

Sample Input 1

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

Sample Output 1

2

For example, if she visits the towns in the order of 1, 2, 3, the distance traveled will be 2, which is the minimum possible.

Sample Input 2

3 3 2
1 3
2 3 2
1 3 6
1 2 2

Sample Output 2

4

The shortest distance between Towns 1 and 3 is 4. Thus, whether she visits Town 1 or 3 first, the distance traveled will be 4.

Sample Input 3

4 6 3
2 3 4
1 2 4
2 3 3
4 3 1
1 4 1
4 2 2
3 1 6

Sample Output 3

3

Solution in Go (1.6) (judge verdict: Wrong Answer)

package main

import (
    "bufio"
    "os"
    "strconv"
    //"strings"
    "fmt"
    "container/heap"
    "math"
)

const INF = 100000000000000000

/*********** PriorityQueue ***********/
type PriorityQueue struct {
    arr []interface{}
    comp CompFunc
}

type CompFunc func(p, q interface{}) bool

func NewPriorityQueue() *PriorityQueue {
    return new(PriorityQueue)
}

func (pq PriorityQueue) Len() int {
    return len(pq.arr)
}

func (pq PriorityQueue) Swap(i, j int) {
    pq.arr[i], pq.arr[j] = pq.arr[j], pq.arr[i]
}

func (pq PriorityQueue) Less(i, j int) bool{
    return pq.comp(pq.arr[i], pq.arr[j])
}

func (pq *PriorityQueue) Push(x interface{}) {
    pq.arr = append(pq.arr, x)
}

func (pq *PriorityQueue) Pop() interface{} {
    n := pq.Len()
    item := pq.arr[n - 1]
    pq.arr = pq.arr[:n - 1]
    return item
}

func (pq *PriorityQueue) IsEmpty() bool {
    return pq.Len() == 0
}

/* type for dijkstra */
type State struct {
    time int
    node int
}

/* type for Edge */
type Edge struct {
    to int
    cost int
}

/* type for bitDp */
type BitAndPos struct {
    bit int
    pos int
}

func (bap *BitAndPos) toHash() int{
    return bap.bit * pow(3, bap.pos)
}

/* math func */
func min(a, b int) int {
    return int(math.Min(float64(a), float64(b)))
}

func pow(a, b int) int {
    return int(math.Pow(float64(a), float64(b)))
}

/* dijkstra */
func dijkstra(start int, n int, edges [][]Edge, comp CompFunc) []int {
    var dist []int
    for i := 0; i < n; i++ {
        dist = append(dist, INF)
    }
    dist[start] = 0
    que := new(PriorityQueue)
    que.comp = comp
    heap.Push(que, State{0, start})
    for !que.IsEmpty() {
        state := heap.Pop(que).(State)
        for _, edge := range edges[state.node] {
            newTime := state.time + edge.cost
            if newTime < dist[edge.to] {
                dist[edge.to] = newTime
                heap.Push(que, State{newTime, edge.to})
            }
        }
    }
    return dist
}

/* bitDp */
func minCost(bap *BitAndPos, dic map[int]int, rDist [][]int, r int) int {
    v, ok := dic[bap.toHash()]
    if ok {
        return v
    }
    if bap.bit == pow(2, r) - 1 {
        return 0
    }

    mask := 1
    ret := INF
    for to := 0; to < r; to++ {
        if bap.bit & mask != 0 {
            mask <<= 1
            continue
        }
        ret = min(ret, rDist[bap.pos][to] + minCost(&BitAndPos{bap.bit | mask, to}, dic, rDist, r))
        mask <<= 1
    }
    dic[bap.toHash()] = ret
    return ret
}


/* input */
var sc = bufio.NewScanner(os.Stdin)

func readInt() int {
    sc.Scan()
    n, _ := strconv.Atoi(sc.Text())
    return n
}

func main() {
    sc.Split(bufio.ScanWords)
    n, m, r := readInt(), readInt(), readInt()

    var rList []int
    for i := 0; i < r; i++ {
        rList = append(rList, readInt() - 1)
    }

    var edges [][]Edge
    for i := 0; i < n; i++ {
        edges = append(edges, make([]Edge, 0))
    }

    for i := 0; i < m; i++ {
        a, b, c := readInt() - 1, readInt() - 1, readInt()
        edges[a] = append(edges[a], Edge{b, c})
        edges[b] = append(edges[b], Edge{a, c})
    }

    comp := func(p, q interface{}) bool {
        return p.(State).time < q.(State).time
    }
    var rDist [][]int
    for i, x := range rList {
        dist := dijkstra(x, n, edges, comp)
        rDist = append(rDist, make([]int, 0))
        for _, y := range rList {
            rDist[i] = append(rDist[i], dist[y])
        }
    }
    dic := make(map[int]int, 0)
    ans := INF
    for i := 0; i < r; i++ {
        ans = min(ans, minCost(&BitAndPos{pow(2, i), i}, dic, rDist, r))
    }
    fmt.Println(ans)
}