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:
inf = float("inf")

class edge():
    def __init__(self, start, target, cost):
        self.start = start
        self.target = target
        self.cost = cost

def bellman_ford(s):
    d = [inf] * V
    d[s] = 0
    cnt = 0
    updateflag = True
    while True:
        updateflag = False
        for i in es:
            if d[i.start] != inf and d[i.target] > d[i.start] + i.cost:
                d[i.target] = d[i.start] + i.cost
                updateflag = True
        if cnt == V-1: return False
        if not updateflag: break
        cnt += 1
    return d

V,E,r = map(int, input().split())
if E == 0: print(0)
else:
 es = [None] * E
 for i in range(E):
     s,t,cost = map(int, input().split())
     es[i] = edge(s, t, cost)
 ans = bellman_ford(r)
 if ans:
     for i in ans:
         if i == inf: print("INF")
         else: print(i)
 else:
    print("NEGATIVE CYCLE")