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:
import queue


class Edge:
    def __init__(self, _to, _cost):
        self.to = _to
        self.cost = _cost


def bellman(n, graph, start):
    dist = [0 if i == start else float('inf') for i in range(n)]

    for i in range(n):
        for v in range(n):
            for e in graph[v]:
                if dist[v] == float('inf') or dist[e.to] <= dist[v] + e.cost:
                    continue

                dist[e.to] = dist[v] + e.cost

                if i == n - 1:
                    return None

    return dist


def main():
    n, m, s = map(int, input().split())
    graph = [[] for _ in range(n)]

    for _ in range(m):
        data = list(map(int, input().split()))

        graph[data[0]].append(Edge(data[1], data[2]))

    ans = bellman(n, graph, s)

    if ans is None:
        print("NEGATIVE CYCLE")
    else:
        for i in range(n):
            print(ans[i] if ans[i] != float('inf') else "INF")
        return


if __name__ == '__main__':
    main()