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<set>
#include<vector>

#define F first
#define S second
#define PB push_back
#define pii pair<int, int>

using namespace std;

const int MAXN = 100005, INF = 1e9;
int d[MAXN];
vector<pii > v[MAXN];
set<pii > s;

void dijkstra(int n, int r)
{
	fill(d, d + n, INF);
	d[r] = 0;
	for(int i = 0; i < n; i++)
		s.insert({d[i], i});
	while(s.size())
	{
		int x = s.begin()->S;
		s.erase(s.begin());
		if(d[x] == INF)
			return;
		for(auto y : v[x])
			if(d[x] + y.S < d[y.F])
			{
				s.erase({d[y.F], y.F});
				d[y.F] = d[x] + y.S;
				s.insert({d[y.F], y.F});
			}
	}
}

int main()
{
	int n, m, r;
	cin >> n >> m >> r;
	for(int i = 0; i < m; i++)
	{
		int x, y, w;
		cin >> x >> y >> w;
		v[x].PB({y, w});
	}
	dijkstra(n, r);
	for(int i = 0; i < n; i++)
		if(d[i] == INF)
			cout << "INF" << endl;
		else
			cout << d[i] << endl;
	return 0;
}