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

int main()
{
	long n, u, k, r, v1, c1;
	const long INF = 0xFFFFFFFF;

	cin >> n >> k >> r;

	vector<vector<long> > v(n), c(n);
	vector<long> w(n, INF);
	typedef pair<long, long> wt;
	priority_queue<wt, vector<wt>, greater<wt> > que;

	for (long i = 0; i < k; i++) {
		cin >> u >> v1 >> c1;
			v[u].push_back(v1);
			c[u].push_back(c1);
	}

	w[r] = 0;
	que.push(wt(0, r));

	while (!que.empty()) {
		wt g = que.top();
		que.pop();

		int k = g.second;

		if (w[k] < g.first)
			continue;

		for (long i = 0; i < (long)v[k].size(); i++) {
			if (w[v[k][i]] > w[k] + c[k][i]) {
				w[v[k][i]] = w[k] + c[k][i];
				que.push(wt(w[v[k][i]], v[k][i]));
			}
		}
	}

	for (long i = 0; i < n; i++) {
		if (w[i] < INF)
			cout << w[i] << endl;
		else
			cout << "INF" << endl;
	}

	return 0;
}