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:
n, m, r = map(int, input().split())
#高速化dijkstra
import heapq
def dijkstra_heap(s,edge):
  d = [float("inf")] * n #始点sから各頂点への最短距離
  used = [False] * n
  d[s] = 0
  used[s] = True
  edgelist = []
  #edgelist : (sからの暫定(未確定)最短距離+頂点)
  #edge[s] : sから出る枝の(重み,終点)の配列
  for w,v in edge[s]:
    heapq.heappush(edgelist,w*10**6+v) #sの隣の点は枝の重さがそのまま暫定最短距離となる
  while len(edgelist):
    #まだ使われてない頂点の中から最小の距離のものを探す→確定させる
    minedge = heapq.heappop(edgelist)
    #minedge : (sからの確定最短距離+頂点)
    v = minedge%10**6
    if used[v]:
      continue
    d[v] = minedge//10**6
    used[v] = True
    for w,u in edge[v]:
      if not used[u]:
        heapq.heappush(edgelist,(d[v]+w)*10**6+u)
  return d

edge = [[] for _ in range(n)]

for i in range(m):
  u,v,w = map(int, input().split())
  edge[u].append((w,v))

d = dijkstra_heap(r,edge)
for ans in d:
    if ans==float('inf'):
        print('INF')
    else:
        print(ans)