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:
#A
#Bellman-Ford法(最短距離)
def BellmanFord(edges,num_v,source):#（辺と重みのリスト、頂点の数、始点(1-index)）
    #グラフの初期化
    inf=float("inf")
    dist=[inf for i in range(num_v)]
    dist[source]=0
    #辺の緩和
    for i in range(num_v):
        for edge in edges:
            if dist[edge[0]] != inf and dist[edge[1]] > dist[edge[0]] + edge[2]:
                dist[edge[1]] = dist[edge[0]] + edge[2]
                if i==num_v-1: 
                  return -1 #負経路を検出
    return dist

V,E,r = map(int,input().split())
STD = [list(map(int,input().split())) for i in range(E)]

inf = float("inf")
dist = BellmanFord(STD,V,r)
if dist == -1:
    print("NEGATIVE CYCLE")
else:
    for d in dist:
        if d == inf:
          print("INF")
        else:
          print(d)