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:
icase=0
if icase==0:
    vv,e,r=map(int,input().split())
    g=[[] for i in range(vv)]
    for i in range(e):
        si,ti,di=map(int,input().split())
        g[si].append((ti,di))
elif icase==1:
    vv,e,r=4,5,0
    g = [[] for _ in range(vv)]
    g[0]=[(1,1),(2,4)]
    g[1]=[(2,2),(3,5)]
    g[2]=[(3,1)]
#ans:0 1 3 4
elif icase==2:
    vv,e,r=4,6,1
    g = [[] for _ in range(vv)]
    g[0]=[(1,1),(2,4)]
    g[1]=[(2,2)]
    g[2]=[(0,1)]
    g[3]=[(1,1),(2,5)]
#ans:3 0 2 INF

from heapq import heappop,heappush

q=[]
heappush(q,(0,r)) 

inf=float("INF")
dist=[inf]*vv
dist[r]=0
while len(q)>0:
    dd,state = heappop(q)
#    print("dd:",dd,"state:",state,"q:",q)
    for v,dv in g[state]:
#        print("v:",v,"dv:",dv,"g[state]:",g[state],"parent[v]:",parent[v])
        if dist[v]>dist[state]+dv:
            dist[v]=dist[state]+dv
            heappush(q,(dist[v],v))
#            print(" state:",state,"v:",v,"dist[v]",dist[v])

for i in range(vv):
    if dist[i]==inf:
        print("INF")
    else:
        print(dist[i])