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 <limits.h>
#include <queue>
#define MAX_V 1000
#define MAX_E 2000
#define INF INT_MAX
using namespace std;

class Edge{
public:
  int from,to,cost;
};
Edge G[MAX_E+1];
int d[MAX_V+1];

int V,E;

int solve(int r){

  fill(d,d+V,INF);
  d[r]=0;
  int cycle=0;
  while(1){
    
    bool update=false;
    
    for(int i=0;i<E;i++){
      Edge e = G[i];
      if(d[e.from]!=INF && d[e.from]+e.cost < d[e.to]){
	d[e.to]=d[e.from]+e.cost;
	update = true;
      }
    }
    if(!update) break;
    cycle++;
    if(cycle>=V) return -1;
  }
 
  return 1;
}


int main(){

  int r;
  cin>>V>>E>>r;
  
  for(int i=0;i<E;i++){
    int from,to,cost;
    cin>>from>>to>>cost;
    G[i].from=from;
    G[i].to=to;
    G[i].cost=cost;
  }
  int ret = solve(r);
  if(ret==-1) cout<<"NEGATIVE CYCLE"<<endl;
  else
    for(int i=0;i<V;i++){
      if(d[i]==INF) cout<<"INF"<<endl;
      else cout<<d[i]<<endl;
    }
  return 0;
}