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;
using i64=int_fast64_t;
using i32=int_fast32_t; 
using P=pair<i64,i64>;
const i64 MOD=1000000007;
const i64 INF=1000000010;
const i64 LINF=4000000000000000010;
int main(){
    struct edge{i32 to;i64 cost;};
    vector<vector<edge>> G;
    vector<i64> di;
    i32 n,m,st;cin>>n>>m>>st;
    G.resize(n);
    di.resize(n);
    for(i32 i=0;i<m;i++){
        i32 u,v,d;cin>>u>>v>>d;
        G[u].push_back({v,d});
    }
    priority_queue<P,vector<P>,greater<P>> q;
    fill(di.begin(),di.end(),LINF);
    di[st]=0;
    q.push(P(0,st));
    while(!q.empty()){
        i32 v=q.top().second;q.pop();
        for(auto e:G[v]){
            if(di[e.to]<=di[v]+e.cost)continue;
            di[e.to]=di[v]+e.cost;
            q.push(P(di[e.to],e.to));
        }
    }
    for(i32 i=0;i<n;i++){
        if(di[i]==LINF){
            cout<<"INF"<<endl;
            continue;
        }
        cout<<di[i]<<endl;
    }
    return 0;
}