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 heapq

n, m, r = list(map(int, input().split()))
V = [i for i in range(n)]
E = [{} for _ in range(n)]

for _ in range(m):
    ef, et, ed = list(map(int, input().split()))
    E[ef][et] = ed
    # E[et][ef] = ed

INF = int(1e18)
dist = {i: INF for i in range(n)}
pred = {i: None for i in range(n)}
dist[r] = 0

update = True
count = 0
while update:
    update = False
    count += 1

    if count > n:
        print("NEGATIVE CYCLE")
        exit()

    for u in range(n):
        for v in E[u]:
            d = E[u][v]
            if dist[u] == INF or dist[u] + d >= dist[v]:
                continue
            else:
                dist[v] = dist[u] + d
                pred[v] = u
                update = True

# check negative cycle
# for u in range(n):
#     for v in E[u]:
#         if dist[u] + E[u][v] < dist[v]:
#             print("NEGATIVE CYCLE")
#             exit(0)

for v in range(n):
    if dist[v] == INF:
        print("INF")
    else:
        print(dist[v])