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 rep(i, n) for (int i = 0; i < (int)(n); i++)
using ll = long long;
using P = pair<int, int>;

#define INF 1001001001

struct Edge {
  int from;
  int to;
  int cost;
};

int main() {
  int n, m, r;
  cin >> n >> m >> r;
  vector<Edge> G;
  rep(i,m) {
    int s, t, d;
    cin >> s >> t >> d;
    G.push_back(Edge({s,t,d}));
  }

  vector<int> d(n,INF);
  d[r] = 0;
  int vcnt = 0;
  while (true) {
    bool update = false;
    rep(i,m) {
      Edge e = G[i];
      if (d[e.from] == INF || d[e.to] <= d[e.from] + e.cost) continue;
      d[e.to] = d[e.from] + e.cost;
      update = true;
    }
    if (!update) break;
    if (++vcnt == n) {
      cout << "NEGATIVE CYCLE" << endl;
      return 0;
    }
  }
  rep(i,n) {
    if (d[i]==INF) cout << "INF" << endl;
    else cout << d[i] << endl;
  }

  return 0;
}