Time Limit : sec, Memory Limit : KB

# Single Source Shortest Path (Negative Edges)

## 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".

## Constraints

• 1 ≤ |V| ≤ 1000
• 0 ≤ |E| ≤ 2000
• -10000 ≤ di ≤ 10000
• There are no parallel edges
• There are no self-loops

## Sample Input 1

4 5 0
0 1 2
0 2 3
1 2 -5
1 3 1
2 3 2


## Sample Output 1

0
2
-3
-1


## Sample Input 2

4 6 0
0 1 2
0 2 3
1 2 -5
1 3 1
2 3 2
3 1 0


## Sample Output 2

NEGATIVE CYCLE


## Sample Input 3

4 5 1
0 1 2
0 2 3
1 2 -5
1 3 1
2 3 2


## Sample Output 3

INF
0
-5
-3