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:
import sys,collections
N,E,r = tuple(map(int,sys.stdin.readline().split())) # single line with multi param
sdw = tuple(tuple(map(int,sys.stdin.readline().rstrip().split())) for _ in range(E)) # multi line with multi param
#sdw = [[src1 dist1 d1][src1 dist1 d1]...]# vect source1 -> distance1 distances
INF = float("inf")
ALL = set(range(N))#including sentinel
distances = collections.defaultdict(lambda:INF)
distances[r] = 0

for _ in range(N):
  modified = False
  for src,dst,weight in sdw:
    if distances[dst] > distances[src] + weight:
      distances[dst] = distances[src] + weight
      modified = True
  if modified == False:
    for i in range(N):
      if distances[i] == INF:
        print("INF")
      else:
        print(distances[i])
    exit()
print("NEGATIVE CYCLE")