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:

v, e, r = map(int, input().split()) # 頂点数v,辺数e,始点rを入力

g = [[] for i in range(v)] # グラフ

for i in range(e):
 s, t, d = map(int, input().split())
 g[s].append([t,d]) # sからtへの辺とその重みd


cost = ['INF' for i in range(v)] # 出力結果を初期化
cost[r] = 0
finish = [] # 最低コストが確定した頂点
finish.append(r)

import heapq
h = []

u = r # 新しく確定した頂点

for count in range(v-1):

 for adj in g[u]:
  if cost[ adj[0] ] != 'INF':
   continue

  new_cost = cost[u] + adj[1]
  heapq.heappush(h, (new_cost, adj[0]))
  

 while 1:
  if len(h) == 0:
   break

  minc = heapq.heappop(h)
  if cost[ minc[1] ] == 'INF':
   cost[ minc[1] ] = minc[0]
   u = minc[1]
   break

for i in range(v):
 print(cost[i])