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;

const int INF=1000000000;

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

int V,E,r;
vector<edge>G[100010];
int d[100010];

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));
            }
        }
    }
}


int main(){
    cin>>V>>E>>r;
    for(int i=0;i<E;i++){
        int a,b,c;
        cin>>a>>b>>c;
        struct edge e;
        e.to=b; e.cost=c;
        G[a].push_back(e);
    }
    dijkstra(r);
    for(int i=0;i<V;i++){
        if(d[i]==INF)cout<<"INF"<<endl;
        else cout<<d[i]<<endl;
    }
    return 0;
}