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
from typing import List, Tuple


if __name__ == "__main__":
    V, E, r = map(lambda x: int(x), input().split())

    edges: List[List[Tuple[int, int]]] = [[] for _ in range(V)]
    dists = [sys.maxsize for _ in range(V)]
    dists[r] = 0

    for _ in range(E):
        s, t, dist = map(lambda x: int(x), input().split())
        edges[s].append((t, dist))

    for _ in range(V):
        for vertex in range(V):
            if sys.maxsize != dists[vertex]:
                for to, cost in edges[vertex]:
                    if cost + dists[vertex] < dists[to]:
                        dists[to] = cost + dists[vertex]

    for vertex in range(V):
        if sys.maxsize != dists[vertex]:
            for to, cost in edges[vertex]:
                if cost + dists[vertex] < dists[to]:
                    # If dist can be smaller than previous one, there is negative cycle.
                    print("NEGATIVE CYCLE")
                    exit(0)

    for dist in dists:
        if sys.maxsize == dist:
            print("INF")
        else:
            print(dist)