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:
import sys
v, e, r = map(int, input().split( ))
E = [[] for _ in range(v)]
inf = 10**12
for _ in range(e):
    s,t,d = map(int, input().split( ))
    E[s].append([t,d])


D = [inf for _ in range(v)]
D[r] = 0
"""
間違い
for ve in range(v):
    for ed in E[ve]:
        D[ed[0]] = min(D[ed[0]], D[ve] + ed[1])
    print(*D)
"""
for _ in range(v):
    for ve in range(v):
        for ed in E[ve]:
            D[ed[0]] = min(D[ed[0]], D[ve] + ed[1])

for i in range(v):
    if E[i]:
        for ed in E[i]:
            if D[i] + ed[1] < D[ed[0]] and D[ed[0]]<inf//10:
                print("NEGATIVE CYCLE")
                sys.exit()

for i in range(v):
    if D[i]<inf//100:
        print(D[i])
    else:
        print("INF")