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;

const int INF = 1 << 29;

struct edge
{
  int u, v, cost;
};

void solve()
{
  int V, E, R;
  cin >> V >> E >> R;
  vector< edge > edges;
  while(E--) {
    int s, t, d;
    cin >> s >> t >> d;
    edges.emplace_back((edge) {s, t, d});
  }
  vector< int > v(V, INF);
  v[R] = 0;

  for(int i = 0; i <= V; i++) {
    for(auto &e : edges) {
      if(v[e.u] == INF) continue;
      if(v[e.u] + e.cost < v[e.v]) {
        v[e.v] = v[e.u] + e.cost;
        if(i == V) {
          cout << "NEGATIVE CYCLE" << endl;
          return;
        }
      }
    }
  }

  for(int i = 0; i < V; i++) {
    if(v[i] >= INF) cout << "INF" << endl;
    else cout << v[i] << endl;
  }
}

int main()
{
  cin.tie(0);
  ios::sync_with_stdio(false);
  solve();
}