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 _GLIBCXX_DEBUG
#define rep(i,n) for(long long i = 0; i < (n); ++i)
#define ll long long
#define P pair<ll,ll>
#define all(v) (v).begin(),(v).end()

const ll mod = 1e9+7;
const ll INF = 1e18;
const double pi = acos(-1.0);

int main(void)
{
    ll v,e,r; cin>>v>>e>>r;
    vector<vector<P>> edges(v);
    rep(i,e){
        ll s,t,d;
        cin>>s>>t>>d;
        edges[s].push_back({d,t});
    }

    vector<ll> dist(v,INF);
    
    priority_queue<P,vector<P>,greater<P>> q;
    q.push({0,r});
    while(!q.empty()){
        P tmp=q.top();
        ll d=tmp.first,t=tmp.second;
        q.pop();
        if(d < dist[t]){
            dist[t] = d;
            for(auto x:edges[t]){
                ll l=x.first,u=x.second;
                if(dist[u] > d+l) q.push({d+l,u});
            }
        }
    }
    
    for(auto d:dist){
        if(d==INF) cout<<"INF"<<endl;
        else cout<<d<<endl;
    }
    return 0;
}