human
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
The above is tricky. Write me a correct solution in PYTHON.
assistant
#Here is Python code to print the cost of the shortest path from the source r to each vertex 0, 1, .

def bellman_ford(vertices, edges, source):
    for v in vertices:
        if v is source:
            v.distance = 0
        else:
            v.distance = Infinity()
        v.predecessor = None
    for _ in xrange(len(vertices)-1):
        for uv in edges:
            u = uv.source
            v = uv.destination
            if v.distance > u.distance + uv.weight:
                v.distance = u.distance + uv.weight
                v.predecessor = u
    for uv in edges:
        u = uv.source
        v = uv.destination
        if u.distance + uv.weight < v.distance:
            raise NegativeCycleError

def main():
    V, E, r = map(int, raw_input().split())
    vertices = [Vertex() for _ in xrange(V)]
    edges = []
    for _ in xrange(E):
        s, t, d = map(int, raw_input().split())
        edges.append(Edge(vertices[s], vertices[t], d))
    try:
        bellman_ford(vertices, edges, vertices[r])
        for v in vertices:
            print v.distance
    except NegativeCycleError:
        print "NEGATIVE CYCLE"

class Infinity(object):
    def __eq__(self, other):
        return other is self

    def __lt__(self, other):
        return False

    def __gt__(self, other):
        return True

    def __add__(self, other):
        return self

    def __radd__(self, other):
        return slef

    def __str__(self):
        return "INF"
    __repr__ = __str__

class NegativeCycleError(Exception):
    pass

class Edge(object):
    def __init__(self, source, destination, weight):
        self.source = source
        self.destination = destination
        self.weight = weight

class Vertex(object):
    def __init__(self, distance=None, predecessor=None):
        self.distance = distance
        self.predecessor = predecessor

if __name__ == "__main__":
    main()