Problem:
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?

Incorrect submission (verdict: Wrong Answer):
from itertools import product


def closest_path_lens(idx___neigh_idxes__dists, idx1):
    INF = 100001 * 201 * 200
    n = len(idx___neigh_idxes__dists)
    idx___visited = [False] * n
    idx___dist = [INF] * n
    idx___dist[idx1] = 0
    for _ in range(n):
        curr_idx = -1
        curr_dist = INF
        for idx, dist in enumerate(idx___dist):
            if dist < curr_dist and not idx___visited[idx]:
                curr_idx = idx
                curr_dist = dist
        idx___visited[curr_idx] = True
        for neigh_idx, dist in idx___neigh_idxes__dists[curr_idx]:
            # print(curr_dist, dist)
            idx___dist[neigh_idx] = min(idx___dist[neigh_idx], curr_dist + dist)
    return idx___dist

def is_valid(path):
    town_idx___visited = [0] * len(list(path))
    zero_dists = 0
    for curr_idx, (idx, dist) in enumerate(path):
        if dist == 0:
            zero_dists += 1
        else:
            town_idx___visited[idx] = 1
            town_idx___visited[curr_idx] = 1
    if zero_dists > 1:
        return False
    elif sum(town_idx___visited) != len(town_idx___visited):
        return False
    else:
        return True

towns_nr, roads_nr, towns_to_visit_nr = (int(x) for x in input().split())
towns_to_visit = [(int(x) - 1) for x in input().split()]
town_idx___neigh_idxes__dists = [set() for _ in range(towns_nr)]
for road_idx in range(roads_nr):
    idx1, idx2, dist = (int(x) for x in input().split())
    idx1 -= 1
    idx2 -= 1
    town_idx___neigh_idxes__dists[idx1].add((idx2, dist))
    town_idx___neigh_idxes__dists[idx2].add((idx1, dist))
ttv_idx___ttv_idx__dist = []
for ttv in towns_to_visit:
    town_idx___dist  = closest_path_lens(town_idx___neigh_idxes__dists, ttv)
    print(town_idx___dist)
    ttv_idx___dist = [town_idx___dist[idx] for idx in towns_to_visit]
    ttv_idx___ttv_idx__dist.append(list(enumerate(ttv_idx___dist)))
ans = 100001 * 201 * 200
for path in product(*ttv_idx___ttv_idx__dist):
    if is_valid(path):
        dists = [x[1] for x in path]
        # print(dists)
        # print(path)
        ans = min(ans, sum(dists))
print(ans)
    


Fixed, accepted submission:
from itertools import permutations
 
 
def closest_path_lens(idx___neigh_idxes__dists, idx1):
    INF = 100001 * 201 * 200
    nodes_nr = len(idx___neigh_idxes__dists)
    idx___visited = [False] * nodes_nr
    idx___dist = [INF] * nodes_nr
    idx___dist[idx1] = 0
    for _ in range(nodes_nr):
        curr_idx = -1
        curr_dist = INF
        for idx, dist in enumerate(idx___dist):
            if dist < curr_dist and not idx___visited[idx]:
                curr_idx = idx
                curr_dist = dist
        idx___visited[curr_idx] = True
        for neigh_idx, dist in idx___neigh_idxes__dists[curr_idx]:
            # print(curr_dist, dist)
            idx___dist[neigh_idx] = min(idx___dist[neigh_idx], curr_dist + dist)
    return idx___dist
 
 
towns_nr, roads_nr, towns_to_visit_nr = (int(x) for x in input().split())
towns_to_visit = [(int(x) - 1) for x in input().split()]
town_idx___neigh_idxes__dists = [set() for _ in range(towns_nr)]
for road_idx in range(roads_nr):
    idx1, idx2, dist = (int(x) for x in input().split())
    idx1 -= 1
    idx2 -= 1
    town_idx___neigh_idxes__dists[idx1].add((idx2, dist))
    town_idx___neigh_idxes__dists[idx2].add((idx1, dist))
ttv_idx___ttv_idx__dist = []
for ttv in towns_to_visit:
    town_idx___dist  = closest_path_lens(town_idx___neigh_idxes__dists, ttv)
    # print(town_idx___dist)
    ttv_idx___dist = [town_idx___dist[idx] for idx in towns_to_visit]
    # print(ttv_idx___dist)
    ttv_idx___ttv_idx__dist.append(ttv_idx___dist)
ans = 100001 * 201 * 200
for path in permutations(list(range(towns_to_visit_nr))):
    curr_ans = 0
    curr_idx = path[0]
    for ttv_idx in path:
        # print(curr_idx, ttv_idx)
        curr_ans += ttv_idx___ttv_idx__dist[curr_idx][ttv_idx]
        curr_idx = ttv_idx
    # print(curr_ans)
    # print('\n')
    ans = min(ans, curr_ans)
print(ans)