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 PYTHON):

Solution:
class Edge():
    def __init__(self, src, to, weight):
        self.src = src
        self.to = to
        self.weight = weight

class NegativeWeightDirectedGraph():
    def __init__(self, V):
        self.V = V
        self.Edges = []
        self.INF = 10**10

    def append(self, src, to, weight):
        self.Edges.append(Edge(src, to, weight))

    def bellmanFord(self, s):
        D = [self.INF] * self.V
        D[s] = 0
        for _ in range(self.V-1):
            for e in self.Edges:
                if D[e.src] != self.INF:
                    w = D[e.src] + e.weight
                    D[e.to] = min(D[e.to], w)
        # check
        for e in self.Edges:
            if D[e.src] == self.INF:
                continue
            if D[e.src] + e.weight < D[e.to]:
                return None
        return D


V,E,r = map(int, raw_input().split())
G = NegativeWeightDirectedGraph(V)
for i in range(E):
    s,t,d = map(int, raw_input().split())
    G.append(s,t,d)

ans = G.bellmanFord(r)
if ans == None:
    print "NEGATIVE CYCLE"
else:
    for d in ans:
        if d == G.INF:
            print "INF"
        else:
            print d