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 sys import stdin
import math
import heapq
#V:num of vertices
#E: num of edges
#r: start vertex
V, E, r = map(lambda x: int(x), stdin.readline().split(' '))

#create adjacency_list
adjacency_list = [[] for x in range(V)] #size V
for i in range(E):
    s, t, d = map(lambda x: int(x), stdin.readline().split(' '))
    adjacency_list[s].append([t, d])

distance = [(math.inf, id) for id in range(V)]
output_distance = [math.inf for id in range(V)]
checked_set = set()
distance[r] = (0, r)

distance.sort()
while len(checked_set) < V:
    target = heapq.heappop(distance)
    target_id = target[1]
    if target_id in checked_set:
        continue
    target_dis = target[0]
    output_distance[target_id] = target_dis
    for i in adjacency_list[target_id]:
        if i[1] + target_dis < output_distance[i[0]]:
            heapq.heappush(distance, ((i[1] + target_dis, i[0])))
    checked_set.add(target_id)
    
for dis in output_distance:
    if dis == math.inf:
        print('INF')
    else:
        print(dis)