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:
import heapq
import math
INF=math.inf
V, E, r = map(int, input().split())
edges = [[] for i in range(V)]
dist = [INF] * V
visited = [0] * V
node_heap=[]
for i in range(E):
    lst = list(map(int, input().strip().split()))
    edges[lst[0]].append([lst[0],lst[1],lst[2]])

dist[r] = 0
cur_node=r     #current_node
visited[r] = 1
#始点ノードから伸びているものに関して追加
for cur_edges in edges[cur_node]:
    heapq.heappush(node_heap,[dist[r]+cur_edges[2],cur_edges[1]]) #(到着ノードまでの総距離,到着のーど)
while node_heap:
    shortest_route = heapq.heappop(node_heap)
    if visited[shortest_route[1]]:
        continue
    cur_node = shortest_route[1]
    dist[cur_node]=shortest_route[0]
    for cur_edges in edges[cur_node]:
        if visited[cur_edges[1]]==0:
            heapq.heappush(node_heap, [dist[cur_node] + cur_edges[2], cur_edges[1]])
    visited[cur_node]=1

for i in range(V):
    if dist[i] == INF:
        print("{}".format("INF"))
    else:
        print("{}".format(dist[i]))