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 ll = long long;

const int MAX_V = 100000;
const ll INF = ll(1e16);

int V, E;
struct edge { int to;ll cost; };
typedef pair<int, int>P;
int N;
vector<edge>G[MAX_V];
ll d[MAX_V];

void dijkstra(int s) {
	priority_queue<P, vector<P>, greater<P>>que;
	fill(d, d + V, INF);
	d[s] = 0;
	que.push(P(0, s));

	while (!que.empty()) {
		P p = que.top();
		que.pop();
		int v = p.second;
		if (d[v] < p.first)continue;
		for (int i = 0; i < G[v].size(); i++) {
			edge e = G[v][i];
			if (d[e.to] > d[v] + e.cost) {
				d[e.to] = d[v] + e.cost;
				que.push(P(d[e.to], e.to));
			}
		}
	}
}
int main()
{
	cin >> V >> E;
	int r;
	cin >> r;
	for (int i = 0; i < E; i++)
	{
		int s, t;
		ll d;
		cin >> s >> t >> d;
		G[s].push_back({t,d});
	}
	dijkstra(r);

	//出力
	for (int i = 0; i < V; i++)
	{
		if (d[i] == INF)
		{
			cout << "INF" << endl;
		}
		else
		{
			cout << d[i] << endl;
		}
	}
	return 0;
}