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:
#計算量ElogV
V,E,r = map(int,input().split()) #頂点数、辺の数，始点
cost = [[] for _ in range(V)] #cost[u][v]がuからvへの距離
INF = float("inf")
d = [INF]* V #頂点ｒから頂点iへの最短重み距離　　　　　
prev = [-1] * V #最短距離をたどるとき、頂点iの一回前に通る頂点
used = [True]*V #Trueは未確定
for _ in range(E):
    s,t,dd = map(int,input().split())
    cost[s].append([dd,t])
d[r] = 0
used[r] = False
import heapq
Q = []
for e in cost[r]:
    heapq.heappush(Q,e)
while len(Q) != 0:
    dis,v = heapq.heappop(Q)
    if used[v] == False:#すでに確定していたら
        continue
    d[v] = dis
    used[v] = False #確定させる
    for e in cost[v]:
        if used[e[1]] == True:#まだ確定していなかったら
            heapq.heappush(Q,[e[0]+d[v],e[1]])
for k in d:
    if k != INF:
        print(k)
    else:
        print("INF")