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 <queue>
#include <algorithm>

#define rep(i, n) for(int i = 0; i < (n); ++i)

using namespace std;

typedef pair<int, int> P;

const int inf = (int)1e9;

struct E{
	E(int t, int c) :
		t(t), c(c)
	{}

	int t, c;
};

int n, m, s;
vector<E> g[(int)1e5];
int d[(int)1e5];

int main(){
	scanf("%d%d%d", &n, &m, &s);
	rep(i, m){
		int a, b, c;
		scanf("%d%d%d", &a, &b, &c);
		g[a].push_back(E(b, c));
	}

	fill(d, d + n, inf);

	priority_queue<P, vector<P>, greater<P> > q;
	d[s] = 0;
	q.push(P(0, s));
	while(!q.empty()){
		P v = q.top();
		q.pop();

		if(v.first > d[v.second]){
			continue;
		}

		rep(i, g[v.second].size()){
			E e = g[v.second][i];
			if(d[e.t] > d[v.second] + e.c){
				d[e.t] = d[v.second] + e.c;
				q.push(P(d[e.t], e.t));
			}
		}
	}

	rep(i, n){
		if(d[i] != inf){
			printf("%d\n", d[i]);
		}
		else{
			puts("INF");
		}
	}
	return 0;
}