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>
#define SIZE 100009
#define INF 1e9
using namespace std;
struct edge{int from,to,cost;};
int n,m,s,d[SIZE],a,b,c,i,j,update;
edge e;
vector<edge>v;

void bellman_ford(){
  fill(d,d+SIZE,INF);d[s]=0;
  for(i=0;i<n;i++){
      update=0;
      for(j=0;j<m;j++){
        e=v[j];
        if(d[e.from]!=INF&&d[e.to]>d[e.from]+e.cost){
            d[e.to]=d[e.from]+e.cost;
            update=1;
            if(i==n-1){
              cout<<"NEGATIVE CYCLE"<<endl;
              return;
            }
        }
    }
    if(!update)break;
  }
  for(i=0;i<n;i++){
    if(d[i]==INF)cout<<"INF"<<endl;
    else cout<<d[i]<<endl;
  }
}
int main(){
  cin>>n>>m>>s;
  for(i=0;i<m;i++){
    cin>>a>>b>>c;
    v.push_back({a,b,c});
  }
  bellman_ford();
}