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 infty = 1e9;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, m, r;
  cin >> n >> m >> r;
  vector<pair<int, pair<int, int> > > grh(m);
  for (int i = 0; i < m; i++) {
    int s, t, d;
    cin >> s >> t >> d;
    grh.push_back({d, {s, t}});
  }
  vector<int> dst(n);
  for (int i = 0; i < n; i++) {
    if (i == r) {
      dst[i] = 0;
    } else {
      dst[i] = infty;
    }
  }
  for (int i = 0; i < n; i++) {
    for (auto e : grh) {
      int d = e.first;
      int s = e.second.first;
      int t = e.second.second;
      if (dst[s] != infty) {
        dst[t] = min(dst[t], dst[s] + d);
      }
    }
  }
  for (auto e: grh) {
    int d = e.first;
    int s = e.second.first;
    int t = e.second.second;
    if (dst[s] != infty && dst[t] > dst[s] + d) {
      cout << "NEGATIVE CYCLE" << '\n';
      return 0;
    }
  }
  for (int i = 0; i < n; i++) {
    if (dst[i] == infty) {
      cout << "INF" << '\n';
    } else {
      cout << dst[i] << '\n';
    }
  }
  return 0;
}