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 PYTHON):

Solution:
import heapq


class Dijkstra(object):
    def dijkstra(self, adj, start, goal=None):
        num = len(adj)
        dist = [float('inf') for i in range(num)]
        prev = [float('inf') for i in range(num)]

        dist[start] = 0
        q = []
        heapq.heappush(q, (0, start))
        
        while len(q) != 0:
            prov_const, src = heapq.heappop(q)

            if dist[src] < prov_const:
                continue

            for i in range(len(adj[src])):
                dest, cost = adj[src][i][0], adj[src][i][1]
                if dist[dest] > dist[src] + cost:
                    dist[dest] = dist[src] + cost
                    heapq.heappush(q, (dist[dest], dest))
                    prev[dest] = src

        if goal is not None:
            return self.get_path(goal, prev)
        else:
            return dist

    def get_path(self, goal, prev):
        path = [goal]
        dest = goal

        while prev[dest] != float('inf'):
            path.append(prev[dest])
            dest = prev[dest]

        return list(reversed(path))

if __name__ == '__main__':
    p_inf = float('inf')
    l = map(int, raw_input().split())
    V, E, r = l[0], l[1], l[2]
    
    adj = [[] for i in range(V)]
    for i in range(E):
        l = map(int, raw_input().split())
        s, t, d = l[0], l[1], l[2]
        adj[s].append((t, d))

    d = Dijkstra()
    result = d.dijkstra(adj, r)
    for i in result:
        if i == p_inf:
            print 'INF'
        else:
            print i