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<functional>
#include<algorithm>
#include<queue>
#include<vector>
#define MM 210000000000000000
using namespace std;
typedef pair<long long,int> P;
vector<int> mati[100000],cost[100000];
int main(void)
{
	int i,n,m,j,b,c,d,p,s,t,r,v,e,flg[100000];
	long long leng[100000],a;

	priority_queue<P,vector<P>,greater<P> > que;
	P ppp;
	scanf("%d %d %d",&v,&e,&r);
	for(i=0;i<e;i++)	{
		scanf("%d %d %d",&s,&t,&d);
		mati[s].push_back(t);
		cost[s].push_back(d);
	}

	for(i=0;i<v;i++)	{
		leng[i]=MM;	flg[i]=0;
	}
	que.push(P(0,r));
	while(que.size()!=0)	{
		ppp=que.top();	que.pop();
		a=ppp.first;	b=ppp.second;
		if(a<leng[b])	{
			leng[b]=a;	flg[b]=1;
			for(i=0;i<mati[b].size();i++)	{
				if(flg[mati[b][i]]==0)	{
					que.push(P(a+cost[b][i],mati[b][i]));
				}
			}
		}
	}
	for(i=0;i<v;i++)	{
		if(leng[i]==MM)	printf("INF\n");
		else printf("%lld\n",leng[i]);
	}
	return 0;
}