Single Source Shortest Path (Negative Edges)

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

inputFormat

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.

outputFormat

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

样例

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

INF
0
-5
-3

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