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:
# https://onlinejudge.u-aizu.ac.jp/problems/GRL_1_B
# 単一始点最短経路（負の重みをもつ辺を含む）

# 初期化、入力の処理
INF = float('inf')
edges = []
V, E, r = map(int, input().split())

for i in range(E):
    s, t, d = map(int, input().split())
    edges.append({"s": s, "t": t, "d": d})

# ベルマンフォード法
ds = [INF for i in range(V)]
ds[r] = 0
i = 0
while True:
    i = i + 1
    update = False
    for j in range(E):
        edge = edges[j]
        if ds[edge["s"]] != INF and ds[edge["t"]] > ds[edge["s"]] + edge["d"]:
            if i == V - 1:
                print("NEGATIVE CYCLE")
                exit()

            ds[edge["t"]] = ds[edge["s"]] + edge["d"]
            update = True
    if not update:
        break

for i in range(V):
    print(ds[i] if ds[i] != INF else "INF")