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 <bits/stdc++.h>
using namespace std;
using Graph = vector<vector<pair<int, int>>>;

int	main()
{
	int	V, E, r;
	cin >> V >> E >> r;
	vector<int64_t>	dist(V, -1);
	Graph	graph(V);
	int	s, t, d;
	for (int i = 0; i < E; ++i) {
		cin >> s >> t >> d;
		graph.at(s).push_back(make_pair(d, t));
	}
	dist.at(r) = 0;
	priority_queue<
		pair<int64_t, int>,
		vector<pair<int64_t, int>>,
		greater<pair<int64_t, int>>
	>	p_que;
	p_que.push(make_pair(0, r));
	int64_t dist_s, cur_dist;
	while (!p_que.empty()) {
		dist_s = p_que.top().first;
		s = p_que.top().second;
		p_que.pop();
		for (auto pr : graph.at(s)) {
			d = pr.first;
			t = pr.second;
			cur_dist = dist_s + d;
			if (dist.at(t) == -1 || dist.at(t) > cur_dist) {
				dist.at(t) = cur_dist;
				p_que.push(make_pair(dist.at(t), t));
			}
		}
	}
	for (int i = 0; i < V; ++i) {
		if (dist.at(i) == -1)
			cout << "INF" << endl;
		else
			cout << dist.at(i) << endl;
	}
}