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<cstdio>
#include<algorithm>
#include<queue>
#include<vector>
using namespace std;
static const int MAX_V = 100000;
static const int INF = 1 << 30;

struct edge{int to, cost;};
typedef pair<int, int> P;

int V;
vector<edge> G[MAX_V];
int 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));
			}
		}
	}
	for(int i = 0; i < V; i++){
		if(d[i] == INF) printf("INF\n");
		else printf("%d\n", d[i]);
	}
}

int main(){
	int E, r;
	scanf("%d %d %d", &V, &E, &r);
	for(int i = 0; i < E; i++){
		int s, t, c;
		scanf("%d %d %d", &s, &t, &c);
		G[s].push_back((edge){t, c});
	}
	dijkstra(r);
	return 0;
}