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:
# Bellman-Ford Algorithm

def bellman_ford(s):
    '''
    始点sから各頂点への最短距離を求める (重み付き有向グラフ)
    '''
    dist = [float('inf')] * v
    dist[s] = 0

    for i in range(v):
        update = False
        for p, q, cost in edge:
            if dist[p] != float('inf') and dist[q] > dist[p] + cost:
                dist[q] = dist[p] + cost
                update = True
        if not update:
            break
        if i == v - 1:  # 負閉路が存在する場合はFalseを返す
            return False

    return dist


################################
v, e, r = map(int, input().split())  # v:頂点数, e:辺の数

edge = []  # edge[i]:[始点,終点,重み]
for _ in range(e):
    s, t, d = map(int, input().split())
    edge.append([s, t, d])

res = bellman_ford(r)

if not res:
    print('NEGATIVE CYCLE')
else:
    for v in res:
        if v == float('inf'):
            print('INF')
        else:
            print(v)