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


def dijkstra(s, edge):
    # 始点sから各頂点への最短距離
    dist = [10**20] * N
    used = [False] * N
    dist[s] = 0
    used[s] = True
    edgelist = []
    for a, b in edge[s]:
        # a : 距離, b : 頂点番号
        heapq.heappush(edgelist, a * (10**6) + b)
    while len(edgelist):
        minedge = heapq.heappop(edgelist)
        # まだ使われてない頂点の中から最小の距離のものを探す
        if used[minedge % (10**6)]:
            continue
        v = minedge % (10**6)
        dist[v] = minedge//(10**6)
        used[v] = True
        for e in edge[v]:
            if not used[e[1]]:
                heapq.heappush(edgelist, (e[0]+dist[v])*(10**6)+e[1])
    return dist


N, M, r = map(int, input().split())
graph = [list(map(int, input().split())) for _ in range(M)]
edge = [[] for _ in range(N)]
for i in graph:
    edge[i[0]].append([i[2], i[1]])

dist = dijkstra(r, edge)
for i in range(N):
    if dist[i] == 10**20:
        print("INF")
    else:
        print(dist[i])