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 PYTHON3):

Solution:
from heapq import heappop as pop
from heapq import heappush as push

INF = 10 ** 18

class edge:
  def __init__(self, to, cost):
    self.to = to
    self.cost = cost

V, E, r = map(int,input().split())

G = [[] for i in range(V)]
#G[i]...頂点iからの辺、(行き先、コスト)
d = [0 for i in range(V)]
#d[i]...スタートからみた頂点iまでの最短距離

def dijkstra(s, V):
  que = []
  global d
  global G
  d = [INF for i in range(V)]
  d[s] = 0
  push(que, (0,s))

  while len(que):
    p = pop(que)
    v = p[1]
    if (d[v] < p[0]):
      continue
#    print(p)
    for i in range(len(G[v])):
      e = G[v][i]
      if d[e.to] > d[v] + e.cost:
        d[e.to] = d[v] + e.cost
        push(que, (d[e.to], e.to))

for i in range(E):
  s, t, c = map(int,input().split())
  G[s].append(edge(t,c))
dijkstra(r, V)

for i in range(V):
  if d[i] != INF:
    print(d[i])
  else:
    print("INF")