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
input = sys.stdin.readline
from operator import itemgetter
sys.setrecursionlimit(10000000)
INF = 10**30

def make_adj_list(n, E):
    l = [[] for _ in range(n)] # 隣接リスト. 各要素は(コスト、to_node)
    for i in range(E):
        s, t, d = map(int, input().strip().split())
        l[s].append([d, t])
    return l

def bellman_ford(n, s, l):
    # s: start node, n: num of node
    # return True: negative cycle
    dist = [INF] * n
    dist[s] = 0
    for i in range(n):
        for v in range(n):
            for k in range(len(l[v])):
                cost, to = l[v][k]
                if dist[v] != INF and dist[to] > dist[v] + cost:
                    dist[to] = dist[v] + cost
                    if i == n-1:
                        return (True, dist)
    return (False, dist)

def main():
    v, e, r = map(int, input().strip().split())
    l = make_adj_list(v, e)
    is_negative_cycle, dist = bellman_ford(v, r, l)
    if is_negative_cycle:
        print("NEGATIVE CYCLE")
        return
    for d in dist:
        if d == INF:
            print('INF')
        else:
            print(d)

if __name__ == '__main__':
    main()