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 bellmanford(G, s):
    n = len(G)
    inf = float('inf')
    dist = [inf] * n
    dist[s] = 0
    for i in range(2*n):
        for v in range(n):
            for w, c in G[v]:
                if dist[w] > dist[v] + c:
                    dist[w] = dist[v] + c
                    if i >= n - 1:
                        return -1
    return dist
import sys
input = sys.stdin.readline

def main():
    inf = float("inf")
    V, E, r = map(int, input().split())
    graph = [[] for _ in range(V)]
    for _ in range(E):
        s, t, d = map(int, input().split())
        graph[s].append((t, d))
    dist = bellmanford(graph, r)
    if dist == -1:
        print("NEGATIVE CYCLE")
    else:
        for d in dist:
            if d == inf:
                print("INF")
            else:
                print(d)

if __name__ == '__main__':
    main()