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:
#https://onlinejudge.u-aizu.ac.jp/courses/library/5/GRL/1/GRL_1_A
import math
import heapq
V,E,r=map(int,input().split())
edge=[[] for _ in range(V)]     # edge[i] : 頂点iからの辺、edge[i][j]:[v,c] 頂点iから頂点vまでの辺、コストc
d=[math.inf for _ in range(V)]  #頂点sからの最短距離

for i in range(E):
    si,ti,di=map(int,input().split())
    edge[si].append([ti,di])
#    edge[ti].append([si,di]) #有向なのでここは無し

#優先度付きキュー
q=[]
heapq.heapify(q)

def dijkstra(start):
    d[start]=0 #初期値
    heapq.heappush(q, [0,start])

    while(len(q)!=0):
        #まだ使われてない頂点のうち距離が最小のものを探す。ない場合は終了
        di=heapq.heappop(q)
        distance=di[0]
        v=di[1]

        if(d[v] < distance):
            continue

        ei = edge[v]
        for i in range(len(ei)):
            e = ei[i]
            if(d[e[0]] > d[v]+e[1]):
                d[e[0]] = d[v]+e[1]
                heapq.heappush(q, [d[e[0]],e[0]])

dijkstra(r)
for i in range(len(d)):
    print(d[i] if d[i]!=math.inf else "INF")