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 PYTHON):

Solution:
import sys

def bellmanford(N, s, graph):
  dist = [sys.maxint] * N
  dist[s] = 0
  for i in xrange(N):
    for v in xrange(N):
      if v not in graph: continue
      for k in xrange(len(graph[v])):
        edge = graph[v][k]
        if dist[v] != sys.maxint and dist[edge[0]] > dist[v] + edge[1]:
          dist[edge[0]] = dist[v] + edge[1]
          if i == N-1: return []
  return dist

V,E,r = map(int, raw_input().split())
graph = {}
for _ in xrange(E):
  s,t,d = map(int, raw_input().split())
  if s not in graph:
    graph[s] = []
  graph[s].append([t,d])
costs = bellmanford(V, r, graph)
if len(costs) == 0:
  print "NEGATIVE CYCLE"
else:
  for i in xrange(V):
    if costs[i] == sys.maxint:
      print "INF"
    else:
      print costs[i]