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 FOR(I,X,Y) for(int I=X;I<Y;I++)
#define REP(I,X,Y) for(int I=Y-1;I>=X;I--)
#define INF 1000000007
#define LINF 1000000000000000007
typedef long long ll;
using namespace std;

int main(){
  int V,E,r,s,t,d;
  cin >> V >> E >> r;
  vector<tuple<int,int,int>> edges;
  ll dmin[V];
  FOR(i,0,V)dmin[i] = LINF;
  dmin[r] = 0;
  FOR(i,0,E){
    cin >> s >> t >> d;
    edges.push_back(make_tuple(s,t,d));
  }
  FOR(i,0,V-1){
    FOR(j,0,E){
      int s=get<0>(edges[j]),t=get<1>(edges[j]),d=get<2>(edges[j]);
      if(dmin[s] != LINF)dmin[t] = min(dmin[t],dmin[s]+d);
    }
  }

  FOR(j,0,E){
    int s=get<0>(edges[j]),t=get<1>(edges[j]),d=get<2>(edges[j]);
    if(dmin[s] != LINF)if(dmin[t] > dmin[s]+d){
      puts("NEGATIVE CYCLE");
      return 0;
    }
  }

  for(auto x:dmin){
    if(x == LINF)puts("INF");
    else cout << x << endl;
  }
}