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())
d=[float("INF")]*v
edges=[[] for i in range(v)]
for i in range(e):
    a,*s=map(int,input().split())
    edges[a].append(s)
d[r]=0
from collections import deque

#pop/append/(append,pop)_left/in/len/count/[]/index/rotate()(右へnずらす)
for i in range(v+2):
    f=False
    used=set()
    dq=deque([r])
    while dq:
        a=dq.popleft()
        for to,c in edges[a]:
            if d[to]>c+d[a]:
                f=True
                d[to]=c+d[a]
            if to not in used:dq.append(to);used.add(to)
    if i==v:print("NEGATIVE CYCLE");exit()
    if f:continue
    break
for i in d:
    print("INF" if i==float("INF") else i)