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 bellman_ford(vertexes, edges, costs, start):
    # cost to each vertex
    d = [float("inf")] * vertexes
    # start cost is zero
    d[start] = 0
    for i in range(vertexes):
        update = False
        for j in range(len(edges)):
            frm, to = edges[j]
            cost = costs[j]
            if d[to] > d[frm] + cost:
                d[to] = d[frm] + cost
                update = True
        # stop if not updated
        if not update:
            break

        # find if closed-loop exists
        if i == n - 1:
            return -1

    return d


n, m, s = map(int, input().split())

edges = []
costs = [-float("inf")] * (m)
score = [-float("inf")] * (n + 1)

for i in range(m):
    a, b, c = map(int, input().split())
    edges.append([a, b])
    costs[i] = c

d = bellman_ford(n, edges, costs, s)

if d == -1:
    print("NEGATIVE CYCLE")
else:
    for i in range(n):
        print(d[i]) if d[i] != float("inf") else print("INF")