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 P pair<int,int>
#define rep(i,n) for(int i=0;i<n;i++)
#define INF 1<<28
#define mk make_pair
using namespace std;
int main(){
  int n,m,t;
  cin>>n>>m>>t;
  vector<pair<int,int> >a[n];
  rep(i,m){
    int q,w,e;
    cin>>q>>w>>e;
    a[q].push_back(mk(w,e));
  }
    priority_queue<P,vector<P>,greater<P> >q;
    int d[n];
    fill(d,d+n,INF);
    q.push(mk(0,t));
    d[t]=0;
    while(!q.empty()){
      P p=q.top();q.pop();
      int v=p.second;
      if(d[v]<p.first)continue;
      for(int i=0;i<a[v].size();i++){
        P ed=a[v][i];
        if(d[ed.first]>d[v]+ed.second){
          d[ed.first]=d[v]+ed.second;
          if(d[ed.first]<-120000)goto L;
          q.push(mk(d[ed.first],ed.first));
        }
      }
    }
  rep(i,n){
    if(d[i]==INF)cout<<"INF"<<endl;
    else cout<<d[i]<<endl;
  }
if(0)L:cout<<"NEGATIVE CYCLE"<<endl;
}