Problem: Constraints

* 1 ≤ |V| ≤ 1000
* 0 ≤ |E| ≤ 2000
* -10000 ≤ di ≤ 10000
* 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

If the graph contains a negative cycle (a cycle whose sum of edge costs is a negative value) which is reachable from the source r, print


NEGATIVE CYCLE


in a line.

Otherwise, print


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 2
0 2 3
1 2 -5
1 3 1
2 3 2


Output

0
2
-3
-1


Input

4 6 0
0 1 2
0 2 3
1 2 -5
1 3 1
2 3 2
3 1 0


Output

NEGATIVE CYCLE


Input

4 5 1
0 1 2
0 2 3
1 2 -5
1 3 1
2 3 2


Output

INF
0
-5
-3

Solution (in CPP):

Solution:
#include <iostream>
#include <vector>
#include <climits>
#define INF (LLONG_MAX>>2)
using namespace std;

typedef long long ll;

class edge{
public:
  int to;
  int weight;
  edge(int to, int weight){
    this->to = to;
    this->weight = weight;
  }
};

void bellmanFord(int, int, vector<edge>*);

int main(){
  int v, e, r;
  cin >> v >> e >> r;

  vector<edge> graph[v];

  int from, to, weight;
  for(int i=0; i<e; i++){
    cin >> from >> to >> weight;
    graph[from].push_back(edge(to, weight));
  }

  bellmanFord(r, v, graph);

  return 0;
}

void bellmanFord(int start, int n, vector<edge>* graph){
  ll d[n];
  for(int i=0; i<n; i++) d[i] = INF;
  d[start] = 0;

  bool neg=false;
  for(int i=0; i<n; i++){
    for(int v=0; v<n; v++){
      for(int k=0; k<graph[v].size(); k++){
        edge e = graph[v][k];
        if(d[v]!=INF && d[e.to] > d[v]+e.weight){
          d[e.to] = d[v]+e.weight;
          if(i==n-1) neg=true;
        }
      }
    }
  }

  if(neg) cout << "NEGATIVE CYCLE" << endl;
  else{
    for(int i=0; i<n; i++){
      if(d[i]==INF) cout << "INF" << endl;
      else cout << d[i] << endl;
    }
  }
}