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:
#配列アクセスを減らした
#入力変更
#出力変更
#tupleで済むところをlistから変更
#変数名以外2907313と同一に見える
import heapq
v, e, r = map(int, input().split( ))
E = [[] for _ in range(v)]
inf = 10**10
for _ in range(e):
    s,t,d = map(int, input().split( ))
    E[s].append((t,d))
D = [inf for _ in range(v)]
#Prev = [-1 for _ in range(v)]
D[r] = 0
Q = []
heapq.heappush(Q, (0,r))
#print(E)
#popからheappopに変更
while Q:
    d,q = heapq.heappop(Q) #qは[距離、頂点番号]：キューの優先度の都合で番号が後
    #print(q)
    for n,c in E[q]:#nは[辺の終点、辺の長さ]
        if D[n]>d+c:
            D[n] = d+c
            #Prev[n] = q
            heapq.heappush(Q, (d+c,n))

for d in D:
    if d<inf:
        print(d)
    else:
        print("INF")