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;
#define MAX 100001
#define inf 1<<30

int n,m,s;
vector<pair<int,int> > e[MAX];

void solve(){
    priority_queue<pair<int,int> > pq;
    int d[MAX];
    fill(d,d+MAX,inf);
    d[s] = 0;
    pq.push(make_pair(0,s));
    while(pq.size()){
        pair<int,int> state = pq.top();
        int v = state.second,cost = -state.first;
        pq.pop();
        if(d[v] < cost)continue;
        
        for(int i=0;i<e[v].size();i++){
            int u = e[v][i].first;
            int n_cost = cost+e[v][i].second;
            if(n_cost<d[u]){
                d[u] = n_cost;
                pq.push(make_pair(-n_cost,u));
            }
        }
    }
    for(int i=0;i<n;i++){
        if(d[i]==inf)cout<<"INF"<<endl;
        else         cout<<d[i]<<endl;
    }
}

int main(){
    cin>>n>>m>>s;
    for(int i=0;i<m;i++){
        int a,b,c;
        cin>>a>>b>>c;
        e[a].push_back(make_pair(b,c));
    }
    solve();
}