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 CPP):

Solution:
#include <algorithm>
#include <climits>
#include <functional>
#include <iostream>
#include <queue>
#include <vector>
using namespace std;

typedef pair<int, int> i_i;
struct edge { int v, w; };

vector<int> dijkstra(int N, vector<vector<edge> >& G, int s) {
	vector<int> d(N, INT_MAX);
	d[s] = 0;
	priority_queue<i_i, vector<i_i>, greater<i_i> > pq;
	pq.push(i_i(0, s));
	while (pq.size()) {
		i_i p = pq.top(); pq.pop();
		int u = p.second;
		if (p.first > d[u]) continue;
		for (edge e: G[u])
			if (d[e.v] > d[u] + e.w) {
				d[e.v] = d[u] + e.w;
				pq.push(i_i(d[e.v], e.v));
			}
	}
	return d;
}


int main() {
	int N, M, s; cin >> N >> M >> s;
	vector<vector<edge> > G(N);
	while (M--) {
		int u, v, w; scanf("%d%d%d", &u, &v, &w);
		G[u].push_back(edge{v, w});
	}
	vector<int> d = dijkstra(N, G, s);
	for (int u = 0; u < N; u++)
		if (d[u] < INT_MAX) printf("%d\n", d[u]);
		else printf("INF\n");
}