def dist_min():
        """
        Gives the nearest node to the origin that is in the set
        """
        min = 10000000
        elem = -1
        for i in range(n):
            if i in set and distTo[i] <= min:
                min = distTo[i]
                elem = i
        return elem

    def neighbors(node):
        """
        Return every neighbor of a node, with the weight of the edge that leads to it
        """
        ret = []
        for (f, t, edge) in paths:
            if f-1 == node:
                weight = edge + tasks[t-1]
                ret.append((t-1, weight))
        return ret

    n = len(tasks)
    distTo = [10000000 for x in range(n)]
    distTo[0] = tasks[0]  # distance to first task is its duration
    set = deque([0])  # set of nodes to explore. contains first task

    while set:  # while set is not empty
        min = dist_min()  # take nearest node to explore
        set.remove(min)  # it has been explored
        for neigh, weight in neighbors(min):  # for all its neighbors
            if distTo[neigh] > distTo[min] + weight:  # if a destination can be reached more quickly:
                distTo[neigh] = distTo[min] + weight  # update that distance
                if not set.__contains__(neigh):
                    set.append(neigh)

    return distTo[n-1]