题目描述
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
输入格式
见题面
输出格式
见题面