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

struct Edge {
  ll from;
  ll to;
  ll cost;
  Edge(ll from, ll to, ll cost) : from(from), to(to), cost(cost) {}
};

using Edges = vector<Edge>;
const ll INF = 1LL << 60;

bool bellman_ford(const Edges &Es, int V, int s, vector<ll> &dis) {
  dis.resize(V, INF);
  dis[s] = 0;
  int cnt = 0;
  while (cnt < V) {
    bool end = true;
    for (auto e : Es) {
      if (dis[e.from] != INF && dis[e.from] + e.cost < dis[e.to]) {
        dis[e.to] = dis[e.from] + e.cost;
        end = false;
      }
    }
    if (end) break;
    cnt++;
  }
  return (cnt == V);
}

int main() {
  int v, e, r;
  cin >> v >> e >> r;
  Edges edges;
  rep(i, e) {
    int s, t, d;
    cin >> s >> t >> d;
    Edge edge(s, t, d);
    edges.push_back(edge);
  }
  vector<ll> dist;
  bool negative = bellman_ford(edges, v, r, dist);

  if (negative) {
    cout << "NEGATIVE CYCLE" << endl;
  } else {
    rep(i, v) {
      if (dist[i] == INF) {
        cout << "INF" << endl;
      } else {
        cout << dist[i] << endl;
      }
    }
  }
}