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>
using namespace std;
#define INF 10000001
int v,e,r,d[1000],cnt;
class edge{
    public:
    int from,to,cost;
};

int main(void){
   cin>>v>>e>>r;
   edge x[e];
   for(int i=0;i<e;i++)cin>>x[i].from>>x[i].to>>x[i].cost;
      
   
   for(int i=0;i<v;i++)d[i]=INF;
   d[r]=0;
   while(1){
       bool update=false;
       for(int i=0;i<e;i++){
           if(d[x[i].from]<INF&&d[x[i].from]+x[i].cost<d[x[i].to]){
               d[x[i].to]=d[x[i].from]+x[i].cost;
               update=true;
           }
       }
       if(update==false)break;
       if(cnt==v-1){
           cout<<"NEGATIVE CYCLE\n";
           return 0;
       }
       cnt++;
   }
    for(int i=0;i<v;i++){
        if(d[i]==INF)cout<<"INF\n";
        else cout<<d[i]<<endl;
    }
}