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:
"""
BellmanFord
"""

INF = 10 ** 20

v_num, e_num, r = map(int, input().split())
dist_lst = [INF for _ in range(v_num)]
edges_lst = [[] for _ in range(e_num)]
negative_cycle_flag = False

for _ in range(e_num):
  s, t, dist = map(int, input().split())
  edges_lst[s].append((dist, t))

dist_lst[r] = 0

if e_num != 0:
  for _ in range(v_num):
    for v in range(v_num):
      if dist_lst[v] != INF:
        for dist, to in edges_lst[v]:
          if dist_lst[v] + dist < dist_lst[to]:
            dist_lst[to] = dist_lst[v] + dist
  
  for v in range(v_num):
    if dist_lst[v] != INF:
      for dist, to in edges_lst[v]:
        if dist_lst[v] + dist < dist_lst[to]:
          negative_cycle_flag = True
          break
      if negative_cycle_flag:
        break

if negative_cycle_flag:
  print("NEGATIVE CYCLE")
else:
  for dist in dist_lst:
    if dist == INF:
      print("INF")
    else:
      print(dist)