Problem: For a given weighted graph G(V, E) and a source r, find the source shortest path to each vertex from the source (SSSP: Single Source Shortest Path).

Constraints

* 1 ≤ |V| ≤ 100000
* 0 ≤ di ≤ 10000
* 0 ≤ |E| ≤ 500000
* There are no parallel edges
* There are no self-loops

Input

An edge-weighted graph G (V, E) and the source r.


|V| |E| r
s0 t0 d0
s1 t1 d1
:
s|E|-1 t|E|-1 d|E|-1


|V| is the number of vertices and |E| is the number of edges in G. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively. r is the source of the graph.

si and ti represent source and target vertices of i-th edge (directed) and di represents the cost of the i-th edge.

Output

Print the costs of SSSP in the following format.


c0
c1
:
c|V|-1


The output consists of |V| lines. Print the cost of the shortest path from the source r to each vertex 0, 1, ... |V|-1 in order. If there is no path from the source to a vertex, print INF.

Examples

Input

4 5 0
0 1 1
0 2 4
1 2 2
2 3 1
1 3 5


Output

0
1
3
4


Input

4 6 1
0 1 1
0 2 4
2 0 1
1 2 2
3 1 1
3 2 5


Output

3
0
2
INF

Solution (in PYTHON):

Solution:
import heapq

class Node():
    def __init__(self, id, w):
        self.id = id
        self.weight = w

    def __str__(self):
        return "id: {}\t weight:{}".format(self.id, self.weight)

    def __lt__(self, other):
        return self.weight < other.weight

class WeightDirectedGraph():    
    def __init__(self, V):
        self.G = {i: [] for i in range(V)}
        self.V = V
        self.INF = 10**10

    def append(self, a, b, w):
        self.G[a].append(Node(b, w))

    def dijkstra(self, s):
        # distance from s
        D = [self.INF] * self.V
        D[s] = 0

        # node with minimum distance
        H = []
        heapq.heappush(H, Node(s, D[s]))

        while len(H) > 0:
            u = heapq.heappop(H)
            if D[u.id] >= u.weight:
                # update distance
                for v in self.G[u.id]:
                    w = u.weight + v.weight
                    if D[v.id] > w:
                        D[v.id] = w
                        heapq.heappush(H, Node(v.id, D[v.id]))
        return D


V,E,r = map(int, raw_input().split())
G = WeightDirectedGraph(V)
for i in range(E):
    s,t,d = map(int, raw_input().split())
    G.append(s,t,d)

for d in G.dijkstra(r):
    if d == G.INF:
        print "INF"
    else:
        print d