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())
std = [ list(map(int,input().split())) for _ in range(e) ]

def BellmanFord(edges,num_v,source):
    #グラフの初期化
    inf = float("inf")
    dist = [ inf for i in range(num_v)]
    dist[source] = 0
    
    #辺の緩和
    for i in range(num_v):
        for edge in edges:
            if edge[0] != inf and dist[edge[1]]>(dist[edge[0]]+edge[2]):
                dist[edge[1]] = dist[edge[0]] + edge[2]
                if i==(num_v-1):
                    return False,[]
    return True,dist

flag,distance = BellmanFord(std,v,r)
# print(flag)
if flag:
    for i in range(v):
        if distance[i]!=float("inf"):
            print(distance[i])
        else:
            print("INF")
else:
    print("NEGATIVE CYCLE")