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:
def main():
    from heapq import heappop, heappush
    INF = 1 << 30

    n, m, r, *E = map(int, open(0).read().split())

    G = [[] for _ in [0]*n]
    for s, t, w in zip(*[iter(E)]*3):
        G[s].append((t, w))

    # Shortest Path Faster Algorithm (SPFA)
    D = [INF]*n
    count = [0]*n
    in_queue = [False]*n
    q = []
    
    D[r] = 0
    count[r] = 1
    in_queue[r] = True
    heappush(q, (0, r))

    while q:
        _, s = heappop(q)
        in_queue[s] = False

        for t, w in G[s]:
            new_d = D[s] + w
            if new_d >= D[t]:
                continue
            D[t] = new_d

            count[t] += 1
            if count[t] >= n:
                print('NEGATIVE CYCLE')
                exit()

            if not in_queue[t]:
                in_queue[t] = True
                heappush(q, (new_d, t))

    print(*['INF' if d == INF else d for d in D], sep='\n')


if __name__ == '__main__':
    main()