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:
def SPFA(G:list, source=0):
	from collections import deque
	V = len(G)
	d = [float("inf")]*V
	inQ = [False]*V
	cnt = [0]*V
	d[source] = 0
	cnt[source] = 1
	Q = deque([source])
	_sum = 0
	_len = 1
	while Q:
		f = Q.popleft()
		inQ[f] = False
		_sum -= d[f]
		_len -= 1
		for t,c in G[f]:
			dist = d[f] + c
			if dist < d[t]:
				d[t] = dist
				if not inQ[t]:
					inQ[t] = True
					cnt[t] += 1
					if dist*_len < _sum:
						Q.appendleft(t)
					else:
						Q.append(t)
					_sum += dist
					_len += 1
				if cnt[t] > V:
					#negative cycle
					return None
	return d
	
def main():
	V,E,r,*L=map(int,open(0).read().split())
	G=[[]for _ in range(V)]
	for s,t,d in zip(*[iter(L)]*3):
		G[s].append((t,d))
	ret = SPFA(G,r)
	if ret==None:
		print("NEGATIVE CYCLE")
	else:
		for x in ret:
			print("INF" if x==float("inf") else x)
			
if __name__=="__main__":main()