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:
# O(EV)
def bellman_ford(s):
    d = [float('inf')]*n # 各頂点への最短距離
    d[s] = 0 # 自身への距離は0
    for i in range(n):
        update = False
        for x, y, z in g:
            if d[y] > d[x] + z:
                d[y] = d[x] + z
                update = True
        if not update:
            break
        # 負閉路が存在
        if i == n - 1:
            return -1
    return d

n, w, s = [int(x) for x in input().split()] # n:頂点数, w:辺の数
g = []
for _ in range(w):
    x, y, z = [int(x) for x in input().split()] # 始点,終点,コスト
    g.append([x, y, z])
d = bellman_ford(s)
if d == -1:
    print("NEGATIVE CYCLE")
else:
    for i in d:
        if i == float("inf"):
            print("INF")
        else:
            print(i)