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 func(r, V, edge):
    c = [float("inf")] * V
    update = True
    loop = 0
    c[r] = 0
    while update:
        update = False
        for s in range(V):
            for t, d in edge[s]:
                temp = c[s] + d
                if temp < c[t]:
                    c[t] = temp
                    update = True

        loop += 1
        if loop == V:
            break
        
    if loop == V and update:
        c[r] = float("inf")

    return c
            

V, E, r = map(int, input().split())
edge = [[] for _ in range(V)]
for _ in range(E):
    s, t, d = map(int, input().split())
    edge[s].append([t, d])

c = func(r, V, edge)

if c[r] == float("inf"):
    print("NEGATIVE CYCLE")
else:
    for temp in c:
        if temp == float("inf"):
            print("INF")
        else:
            print(temp)