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 rep(i, n) for(int i=0; i<n; i++)
#define INF 1000000000

struct edge{
  int to, cost;
  edge(int to, int cost):
    to(to), cost(cost){}
};
struct vertex{
  vector<edge> V;
};

vertex G[1000];
int ne, nv, r;
int d[1000];

bool bellman(int s){
  fill(d, d+nv, INF);
  d[s]=0;
  rep(p, nv){
    bool update=false;
    rep(i, nv){
      rep(j, G[i].V.size()){
	edge e=G[i].V[j];
	if(d[i]!=INF && d[i]+e.cost<d[e.to]){
	  d[e.to]=d[i]+e.cost;
	  update=true;
	}
      }
    }
    if(!update)break;
    if(p==nv-1)return false;//?????????
  }
  return true;
}

int main(){
  cin>>nv>>ne>>r;
  rep(i, ne){
    int s, t, d;
    cin>>s>>t>>d;
    G[s].V.push_back(edge(t, d));
  }
  if(bellman(r)){
    rep(i, nv)
      if(d[i]==INF)cout<<"INF"<<endl;
      else cout<<d[i]<<endl;
  }
  else{
    cout<<"NEGATIVE CYCLE"<<endl;
  }
  return 0;
}