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:
num_v,num_e,source=input().split()

edges=[]
verticies=[]

for i in range(int(num_e)):
    v,u,w=input().split()
    e=(int(v),int(u),int(w))
    edges.append(e)


for v in range(int(num_v)):
    v=str(v)
    verticies.append(v)

itn=int(num_v)-1
g=edges

dist=[float('inf')]*(itn+1)
dist[int(source)]=0


def BF(g):
    for i in range(itn):
        for edge in edges:
            v,u,w =edge
            if dist[v]!=float('inf'):
                if dist[v] + w < dist[u]:
                    dist[u]=dist[v] + w
                    
    #check negative cycle
    ngc=0
    for edge in edges:
        v,u,w=edge
        if dist[v]!=float('inf'):
            if dist[v] + w < dist[u]:
                ngc=1
                 
                
    if ngc==0:
        for i in range(itn+1):
            if dist[i]==float('inf'):
                print("INF")
            else: print(dist[i])
    else:
        print("NEGATIVE CYCLE")

BF(g)