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;
typedef long long ll;
#define REP(i,n) FOR(i,0,n)
#define FOR(i,a,b) for(ll i=a;i<b;i++)
#define PB push_back
typedef vector<ll> vi;
typedef vector<vector<ll>> vvi;
const ll INF = (1ll << 60);
typedef pair<ll,ll> pii;
struct Edge{ll s,t,d;};
typedef vector<vector<Edge>> Graph;


int main(){
  ll V,E,r; cin>>V>>E>>r;
  vector<Edge> edges(E);
  REP(i,E) cin>>edges[i].s>>edges[i].t>>edges[i].d;
  Graph graph(V);
  for(Edge edge:edges) graph[edge.s].PB(edge);
  vi dist(V,INF);
  dist[r]=0;
  for(int cnt=0;;cnt++){
    REP(i,V) for(Edge e:graph[i]){
      if(dist[e.s]==INF) continue;
      if(dist[e.t]>dist[e.s]+e.d){
        dist[e.t]=dist[e.s]+e.d;
        if(cnt>V){
          cout<<"NEGATIVE CYCLE"<<endl;
          return 0;
        }
      }
    }
    if(cnt>V) break;
  }
  for(ll d:dist) if(d==INF) cout<<"INF"<<endl; else cout<<d<<endl;
}