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:
# -*- coding: utf-8 -*-
import Queue
INF = 10000000000000000

# ?¨??????\???????????\????????¢?????§????????????
# |V| |E|
# ai bi wi
V,E,r = map(int,raw_input().split())
edges = [[] for i in range(V)]	# ??£??\?????????

for i in xrange(E):
	a,b,w = map(int,raw_input().split())
	edges[a].append({'to':b,'weight':w})
	# edges[b].append({'to':a,'weight':w})

distance = [INF] * V
visited = [False] * V

distance[r] = 0
pq = Queue.PriorityQueue()
pq.put((0,r))
while not pq.empty():
	d,v = pq.get()
	visited[v] = True
	for e in edges[v]:
		if visited[e['to']] or distance[v]+e['weight'] > distance[e['to']]: continue
		distance[e['to']] = distance[v] + e['weight']
		pq.put((d+e['weight'],e['to']))

for d in distance:
	if d >= INF:
		print "INF"
	else:
		print d

# for i in range(V):
# 	min_v = -1
# 	for v in range(V):
# 		if not visited[v] and (min_v == -1 or distance[v] < distance[min_v]):
# 			min_v = v

# 	visited[min_v] = True
# 	for e in edges[min_v]:
# 		distance[e['to']] = min(distance[min_v] + e['weight'],distance[e['to']])

# for d in distance:
# 	if d >= INF:
# 		print "INF"
# 	else:
# 		print d