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;
using ll=long long;

struct Edge{
  int to;
  int weight;
  Edge(int t,int w) : to(t),weight(w){}
};

using Graph = vector<vector<Edge>>;

int main(){
  int n,m,r;
  cin >> n >> m >> r;
  Graph G(n);

  for(int i=0;i<m;++i){
    int from,to,weight;
    cin >> from >> to >> weight;
    G[from].push_back(Edge(to,weight));
  }
  vector<ll> dist(n,1001001);
  vector<int> cnt(n,0);
  queue<int> que;
  dist[r]=0;
  cnt[r]=1;
  que.push(r);
  while(!que.empty()){
    int v=que.front();
    que.pop();
    for(auto nv : G[v]){
      if(dist[nv.to] == 1001001 || dist[nv.to] > dist[v]+nv.weight){
        if(dist[nv.to]<0 && cnt[nv.to]>m){
          cout << "NEGATIVE CYCLE" << endl;
          return 0;
        }
        dist[nv.to] = dist[v]+nv.weight;
        cnt[nv.to]++;
        que.push(nv.to);
      }
    }
  }
  for(int i=0;i<n;++i){
    if(dist[i]==1001001) cout << "INF" << endl;
    //else if(dist[i]<0) cout << "NEGATIVE CYCLE" << endl;
    else cout << dist[i] << endl;
  }
  return 0;

}