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:
# -*- coding: utf-8 -*-
"""
http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_1_B&lang=jp

"""
import sys
from sys import stdin
from collections import namedtuple
input = stdin.readline


def shortest_path(es, V, s):
    count = 0
    d = [float('inf')] * V
    d[s] = 0

    while True:
        update = False
        count += 1

        if count > V:
            return None

        for e in es:
            if d[e.f] != float('inf') and d[e.t] > d[e.f] + e.c:
                d[e.t] = d[e.f] + e.c
                update = True
        if update is False:
            break

    for i, dist in enumerate(d):
        if dist == float('inf'):
            d[i] = 'INF'
    return d


edge = namedtuple('edge', ['f', 't', 'c'])
def main(args):
    V, E, r = map(int, input().split())
    es = []
    for _ in range(E):
        s, t, d = map(int, input().split())
        es.append(edge(s, t, d))

    result = shortest_path(es, V, r)

    if result is None:
        print('NEGATIVE CYCLE')
    else:
        print('\n'.join(map(str, result)))


if __name__ == '__main__':
    main(sys.argv[1:])