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 sys
import heapq as h

inf = sys.maxsize

# おまじない
class heapq:
    def __init__(self):
        self.q = []

    def push(self,v):
        h.heappush(self.q, v)
    
    def pop(self):
        return h.heappop(self.q)

    def is_empty(self):
        return len(self.q) == 0


V,e,r=(int (i)for i in input().split())
#print(v)
G=[[] for i in range(V)]#iごとに[]（式）を評価(実行)する。
for j in range(e):
    f,t,cost=(int (i)for i in input().split())
    G[f].append((t,cost))
dist=[inf]*100000
visited=[False]*100000
a=heapq()
a.push((0,r))
def end(visited):
    for i in visited:
        if i==False:
            return False
    return True
while(not a.is_empty()):
    (cur_dist,u)=a.pop()#uはid,cur_distはいまの道の長さ
    if not visited[u]:
        
        dist[u]=cur_dist
        #print(cur_dist,u)
        visited[u]=[True]
        for (v,cost) in G[u]:
            if not visited[v] and dist[u]+cost<dist[v]:
                a.push((dist[u]+cost,v))
#print(v)
for i in range(V):
    if dist[i]==inf:
        print('INF')
    else:
        print(dist[i])