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 <cstdio>
#include <vector>
#include <algorithm>
using namespace std;

#define INF 10000000
#define MAX_V 1000

int V,E;
struct edge{int from,to,cost;};
vector<edge> edges;
int d[MAX_V];
int main(){
  int f,t,c;
  int s;
  scanf("%d %d %d",&V,&E,&s);
  for(int i=0;i<E;i++){
    scanf("%d %d %d",&f,&t,&c);
    edge es;
    es.from=f;es.to=t;es.cost=c;
    edges.push_back(es);
  }
  fill(d,d+V,INF);
  d[s]=0;
  for(int i=0;i<V;i++){
   
    for(int j=0;j<E;j++){
      edge e=edges[j];
      if(d[e.from]!=INF && d[e.to] > d[e.from]+e.cost){
	d[e.to]=d[e.from]+e.cost;
	if(i==V-1){
	  printf("NEGATIVE CYCLE\n");
	  return 0;
	}
      }
    }
  }
  for(int x=0;x<V;x++){
    if(d[x]!=INF) printf("%d\n",d[x]);
    else printf("INF\n");
  }
  return 0;
}