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:
INF=10**30
def Belman_Ford(s,N):
    dist=[INF]*N
    dist[s]=0
    cnt=0
    neg=False
    while True:
        if cnt==N:
            break
        update=False
        for f,t,c in Edge:
            if dist[t]>dist[f]+c:
                if cnt<N-1:
                    if dist[f]!=INF:
                        dist[t]=min(dist[t],dist[f]+c)
                        update=True
                else:
                    neg=True
        if not update:
            break
        cnt+=1
    if neg:
        return -1
    else:
        return dist
        
V,E,r=map(int,input().split())
Edge=[tuple(map(int,input().split())) for i in range(E)]

res=Belman_Ford(r,V)
if type(res) is int:
    print('NEGATIVE CYCLE')
else:
    for i in range(V):
        print(res[i] if res[i]!=INF else 'INF')