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 bellman_ford():
    edges = []
    inf = 1

    n, m, s = map(int, input().split())

    for i in range(m):
        src, tgt, cost = map(int, input().split())
        edges.append({'source': src, 'target': tgt, 'cost': cost})
        if cost > 0:
            inf += cost

    graph = [{'cost': inf, 'source': -1} for i in range(n)]
    graph[s]['cost'] = 0

    for i in range(n - 1):
        for edge in edges:
            src = edge['source']
            tgt = edge['target']
            if graph[src]['cost'] == inf:
                continue
            if graph[tgt]['cost'] > graph[src]['cost'] + edge['cost']:
                graph[tgt]['cost'] = graph[src]['cost'] + edge['cost']
                graph[tgt]['source'] = src

    for edge in edges:
        src = edge['source']
        tgt = edge['target']
        if graph[src]['cost'] == inf:
            continue
        if graph[tgt]['cost'] > graph[src]['cost'] + edge['cost']:
            print('NEGATIVE CYCLE')
            return

    for vertex in graph:
        print(vertex['cost']) if vertex['cost'] < inf else print('INF')


bellman_ford()