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

inf = sys.maxsize*1000000
V,e,r=(int (i)for i in input().split())
NC=False
#print(v)
#G=[[] for i in range(V)]#iごとに[]（式）を評価(実行)する。
G=[]
for j in range(e):
    f,t,cost=(int (i)for i in input().split())
    G.append((f,t,cost))
dist=[inf for _ in range(100000)]

dist[r]=0
max_=0
for i in range(V):
    for (u,v,cost) in G:#辺をひとつづつ追加していって最短距離の更新を試みる？

        if dist[u]!=inf and dist[u]+cost<dist[v]: 
            if i==V-1:
               
                NC=True
            else:
                dist[v]=dist[u]+cost

        
if not NC:
    for i in range(V):
        if dist[i]>=inf/2:
            print('INF')
        else:
            print(dist[i])
else:
     print("NEGATIVE CYCLE")