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;
#define endl '\n'
#define MOD 1000000007LL
#define REP(i, n) for(int i=0;i<(n);++i)
typedef long long ll;

#define INF 2000000000
int V, E, r;
typedef pair<int, int> P;
struct edge {int to, cost;};
vector<edge> graph[100000];
int d[100000];

void dijkstra(int s){
	fill(d, d+V, INF); d[s] = 0;
	priority_queue<P, vector<P>, greater<P> > que;
	que.push(P(0, s));
	while(!que.empty()){
		P a = que.top(); que.pop();
		if(d[a.second] < a.first) continue;
		REP(i, graph[a.second].size()){
			edge e = graph[a.second][i];
			if(d[e.to] > d[a.second]+e.cost){
				d[e.to] = d[a.second]+e.cost;
				que.push(P(d[e.to], e.to));
			}
		}
	}
}

signed main(){
	cin.tie(0);
	ios::sync_with_stdio(false);

	cin >> V >> E >> r;
	REP(i, E){
		int s, t, d; cin >> s >> t >> d;
		graph[s].push_back({t, d});
	}
	dijkstra(r);
	REP(i, V){
		if(d[i] == INF) cout << "INF" << endl;
		else cout << d[i] << endl;
	}

	return 0;
}