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 <iostream>
#include <vector>
using namespace std;

void shortest_path(int);

#define MAX_E 500000
#define MAX_V 100000

typedef long long ll;

const ll INF = 1e10;

struct edge {
  ll from; //何処から
  ll to;   //何処へ
  ll cost; //重み
};

edge es[MAX_E];  //辺

ll l[MAX_V];

ll V;  //頂点数
ll E;  //辺の数
ll r;  //始点

int main() {

  ll s, t, d;

  cin >> V >> E >> r;

  for(int i=0; i<E; ++i) {
    cin >> s >> t >> d;
    es[i].from = s;
    es[i].to = t;
    es[i].cost = d;
  }

  shortest_path(r);

  return 0;
}

void shortest_path(int s) {

  for(int i=0; i<V; ++i) l[i] = INF;

  l[s] = 0;

  while(true) {
    bool update = false;

    for(int i=0; i<E; ++i) {
      edge e = es[i];

      if(l[e.from] != INF && l[e.to] > l[e.from] + e.cost) {
        l[e.to] = l[e.from] + e.cost;
        update = true;
      }
    }
    if(!update) break;
  }

  for(int i=0; i<V; ++i) {
    if(l[i]==INF) cout << "INF" << endl;
    else cout << l[i] << endl;
  }
}