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 MAX_V 1111
#define MAX_E 2222
#define INF 1111111111
struct edge{int from,to,cost;};

edge es[MAX_E]; //辺
int d[MAX_V]; //最短距離
int V,E; //頂点数、辺数

//最短距離を求める
int shortest_path(int s){
  fill(d,d+V,INF);
  d[s]=0;
  int cnt=0;
  while(1){
    bool update=false;
    for(int i=0;i<E;i++){
      edge e=es[i];
      if(d[e.from]!=INF&&d[e.to]>d[e.from]+e.cost){
	d[e.to]=d[e.from]+e.cost;
	update=true;
      }
    }
    if(!update)break;
    cnt++;
    if(cnt==V)return 0;
  }
  return 1;
}

int main(){
  int r;
  cin>>V>>E>>r;
  for(int i=0;i<E;i++)
    cin>>es[i].from>>es[i].to>>es[i].cost;
  if(shortest_path(r)){
    for(int i=0;i<V;i++){
      if(d[i]==INF)cout<<"INF"<<endl;
      else cout<<d[i]<<endl;
    }
  }else cout<<"NEGATIVE CYCLE"<<endl;
  return 0;
}