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;

template<typename T> struct Graph {
  struct Edge { int from, to; T cost; };
  size_t n;
  vector<T> dist;
  vector<int> hasPath;
  vector<Edge> es;
  Graph(size_t n_, T INF) : n(n_), dist(n_, INF + INF), hasPath(n_, 0), es(n_) {}

  void addEdge(int u, int v, T w) {
    es.push_back({u, v, w});
    //g[v].push_back({u, w});
  }
  bool bellmanFord(int s) {
    dist[s] = 0;
    hasPath[s] = 1;
    for (int i = 0; i < n; ++i) {
      for (auto&& e : es) {
        if (dist[e.to] > dist[e.from] + e.cost) {
          dist[e.to] = dist[e.from] + e.cost;
          hasPath[e.to] |= hasPath[e.from];
          if (i == n - 1 && hasPath[e.to]) return false;
        }
      }
    }
    return true;
  }
};

const int INF = 1e9;

int main() {
  int n, m, r; cin >> n >> m >> r;
  Graph<int> g(n, INF);
  while (m--) {
    int s, t, d; cin >> s >> t >> d;
    g.addEdge(s, t, d);
  }
  if (!g.bellmanFord(r)) {
    cout << "NEGATIVE CYCLE" << endl;
  } else {
    for (int i = 0; i < n; ++i) {
      cout << ( (g.dist[i] >= INF || !g.hasPath[i]) ? "INF" : to_string(g.dist[i]) ) << endl;
    }
  }
  return 0;
}