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

stdin = sys.stdin

ns = lambda : stdin.readline().rstrip()
ni = lambda : int(ns())
na = lambda : list(map(int, stdin.readline().split()))

INF = int(1e18)

class BellmanFord:
  N = -1
  edge = []
  
  def __init__(self, N):
    self.N = N
  
  def addEdge(self, a, b, cost):
    self.edge.append((a, b, cost))
  
  def addBiEdge(self, a, b, cost):
    self.addEdge(a, b, cost)
    self.addEdge(b, a, cost)

  def calc(self, start):
    dist = [INF] * self.N
    dist[start] = 0
    update = True
    cnt = 0
    while update:
      update = False
      cnt += 1
      if cnt > self.N:
        return -INF
      for a, b, cost in self.edge:
        ncost = dist[a] + cost
        if dist[a] == INF or ncost >= dist[b]:
          continue
        dist[b] = ncost
        update = True
    return dist

def main():
  v, e, r = na()
  BF = BellmanFord(v)
  for _ in range(e):
    BF.addEdge(*na())

  ans = BF.calc(r)
  if ans == -INF:
    print("NEGATIVE CYCLE")
  else:
    for i in range(v):
      print('INF' if ans[i] == INF else ans[i])

main()