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:
INF = float("inf")


def bellman_ford(edges, num_v, sv):
    #グラフの初期化
    dist = [INF for i in range(num_v)]
    dist[sv]=0
    
    #辺の緩和
    for i in range(num_v):
        for edge in edges:
            s, t, d = edge[0], edge[1], edge[2]
            if dist[s] != INF and dist[t] > dist[s] + d:
                dist[t] = dist[s] + d
                if i == num_v - 1:
                    return -1       # 負の閉路が存在する
    
    return dist


def main():
    N, M, r = map(int, input().split())

    edges = []
    for _ in range(M):
        s, t, d = map(int, input().split())
        edges.append([s, t, d])
    
    dist = bellman_ford(edges, N, r)
    if dist == -1:
        print("NEGATIVE CYCLE")
    else:
        for i in range(N):
            ans = dist[i]
            if ans == INF:
                ans = "INF"
            print(ans)


if __name__ == '__main__':
    main()