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 sys
readline = sys.stdin.readline

V, E, r = map(int, readline().split())
inf = 10**10
edges = [[] for _ in [None]*V]

for _ in [None]*E:
    s, t, d = map(int, readline().split())
    edges[s].append((t, d))


def bellman_ford(n, edges, start):
    vertices = [inf] * n
    vertices[start] = 0
    reached = {start}

    for i in range(n):
        flag = 0
        for v in reached.copy():
            cost = vertices[v]
            for dist, _cost in edges[v]:
                newcost = cost + _cost
                if vertices[dist] > newcost:
                    vertices[dist] = newcost
                    reached.add(dist)
                    flag = 1
        if flag == 0:
            return vertices
    else:
        return None

result = bellman_ford(V, edges, r)
if result:
    print("\n".join([str(n) if n!=inf else "INF" for n in result]))
else:
    print("NEGATIVE CYCLE")