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<bits/stdc++.h>
using namespace std;

#define INF (1<<30)
typedef pair< int , int > P;
struct Edge {
  int to,cost;
  Edge(){}
  Edge(int to,int cost):to(to),cost(cost){};
};
vector< vector< Edge > > Graph;
vector< int > min_cost;
int V,E;

bool Bellman_Ford(int s){
  min_cost.assign(Graph.size()+1,INF);
  bool negative_loop = false;
  min_cost[s] = 0;
  for(int k=0;k<V;k++){
    for(int i=0;i<V;i++){
      for(int j=0;j<Graph[i].size();j++){
	if(min_cost[i] == INF) continue;
	Edge e = Graph[i][j];
	if(min_cost[e.to] > min_cost[i]+e.cost){
	  min_cost[e.to] = min_cost[i]+e.cost;
	  if(k == V - 1){
	    min_cost[e.to] = -INF;
	    negative_loop = true;
	  }
	}
      }
    }
  }
  return negative_loop;
}

int main(){
  int r;
  cin >> V >> E >> r;
  Graph.resize(V+1);
  for(int i=0;i<E;i++){
    int s,t,d;
    cin >> s >> t >> d;
    Graph[s].push_back(Edge(t,d));
    //Graph[t].push_back(Edge(s,d));
  }
  bool flg = Bellman_Ford(r);
  if(flg) cout << "NEGATIVE CYCLE" << endl;
  else {
    for(int i=0;i<V;i++){
      if(min_cost[i] == INF) cout << "INF" << endl;
      else cout << min_cost[i] << endl;
    }
  }
}