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;

template<typename T>
struct E{
  int from,to;
  T cost;
};

template<typename T>
vector<T>bellman_ford(vector<E<T>>&g,int s,int sz){
  T inf=numeric_limits<T>::max();
  vector<T>d(sz,inf);
  d[s]=0;
  for(int i=0;i<sz-1;i++)for(auto e:g)if(d[e.from]!=inf)d[e.to]=min(d[e.to],d[e.from]+e.cost);
  for(auto e:g)if(d[e.from]!=inf&&d[e.from]+e.cost<d[e.to])return vector<T>();
  return d;
}

int main(){
  int N,M,S;
  cin>>N>>M>>S;
  vector<E<int>>G(M);
  for(int i=0;i<M;i++){
    int a,b,c;
    cin>>a>>b>>c;
    G[i]={a,b,c};
  }
  vector<int>ans=bellman_ford<int>(G,S,N);
  if(ans==vector<int>())cout<<"NEGATIVE CYCLE"<<endl;
  else for(auto it:ans){
    if(it==numeric_limits<int>::max())cout<<"INF"<<endl;
    else cout<<it<<endl;
  }
}