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:
V, E, r = map(int, input().split())
nodes = [list(map(int, input().split())) for _ in range(E)] #e = from, to, cost

def shortest_path(s):
    d = [float('inf') for i in range(V)]
    d[s] = 0
    for _ in range(V):
        update = False
        for i in range(E):
            e = nodes[i]
            if d[e[0]] != float('inf') and d[e[1]] > d[e[0]] + e[2]:
                d[e[1]] = d[e[0]] + e[2]
                update = True
    if update:
        return None
    else:
        return d

if not shortest_path(r):
    print('NEGATIVE CYCLE')
else:
    d = shortest_path(r)
    for i in range(V):
        if d[i] == float('inf'):
            print('INF')
        else:
            print(d[i])