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 heapq import *
def dijkstra(s, n, w, cost):
    #s:始点,n:頂点数,w:辺の数,cost:辺ijの重み
    ans = [float('inf')] * n #最短距離の記録
    d = [[float('inf'), i] for i in range(n)]
    used = [False] * n #一度最短距離を確定した頂点はもう見ない
    ans[s] = 0
    d[s][0] = 0
    heapify(d)

    while d:
        D, V = heappop(d)
        if used[V]:continue
        used[V] = True

        for t, distance in cost[V]:
            ans[t] = min(ans[t], D + distance)
            heappush(d, [ans[t], t])
    return ans

v, e, r = map(int,input().split())
route_list=[[] for i in range(v)]#辺の移動の際のコスト

for i in range(e):
    s,t,d=map(int,input().split())
    route_list[s].append((t,d))
#print(route_list)

ans = dijkstra(r, v, e, route_list)

for i in ans:
    if i == float('inf'):
        print('INF')
    else:
        print(i)