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>
#define REP(i,n) for(int i=0;i<(n);i++)
#define ALL(v) (v).begin(),(v).end()
#define int long long
using namespace std;
typedef vector<int>   vint;
typedef pair<int,int> pint;

struct edge{int to,cost;};
const int inf=1e9;

int N,M;
vector<edge> G[100010];

vint dijkstra(int s)
{
    vint dist(N,inf); dist[s]=0;
    priority_queue<pint,vector<pint>,greater<pint> >Q;
    Q.push(pint(0,s));

    while(!Q.empty())
    {
	pint p=Q.top(); Q.pop();
	int v=p.second;
	if(p.first>dist[v]) continue;

	for(auto e:G[v]){
	    if(dist[e.to]>dist[v]+e.cost){
		dist[e.to]=dist[v]+e.cost;
		Q.push(pint(dist[e.to],e.to));
	    }
	}
    }
    return dist;
}

signed main()
{
    int s; cin>>N>>M>>s;
    REP(i,M){
	int a,b,c; cin>>a>>b>>c;
	G[a].push_back((edge){b,c});
    }

    vint dist=dijkstra(s);
    REP(i,N){
	if(dist[i]==inf) cout<<"INF"<<endl;
	else cout<<dist[i]<<endl;
    }

}