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())
edges = []
for _ in range(e):
    s, t, d = map(int, input().split())
    edges.append((s, t, d))

def shortest_path(v, s, edges, inf):
    d = [inf] * v
    d[s] = 0
    cnt = 0
    while True:
        cnt += 1
        update = False
        for frm, to, cost in edges:
            if d[frm] != inf and d[to] > d[frm] + cost:
                d[to] = d[frm] + cost
                update = True
        if cnt == v and update:
            return False
        elif not update:
            break
    return d

inf = 10 ** 9
d = shortest_path(v, r, edges, inf)
if d == False:
    print('NEGATIVE CYCLE')
else:
    for i in range(v):
        if d[i] == inf:
            print('INF')
        else:
            print(d[i])