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 PYTHON3):

Solution:
INF = float('inf')

def bellman_ford(graph, weights, s):
  d = {v: INF for v in graph}
  d[s] = 0
  edges = [(u, v) for u, vs in graph.items() for v in vs]
  for _ in range(len(graph) - 1):
    for (u, v) in edges:
      d_temp = d[u] + weights[u, v]
      if d_temp < d[v]:
        d[v] = d_temp

  for (u, v) in edges:
    if d[u] + weights[u, v] < d[v]:
      print('NEGATIVE CYCLE')
      return None
  return d


n_vertex, n_edge, s = [int(x) for x in input().split()]
graph = {i: [] for i in range(n_vertex)}
weights = {}
for i in range(n_edge):
    u, v, w = [int(x) for x in input().split()]
    graph[u].append(v)
    weights[u, v] = w

d = bellman_ford(graph, weights, s)

if d is not None:
    for i in range(n_vertex):
        print(d[i] if d[i] is not INF else 'INF')