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:
#!/usr/bin/env python3
# -*- coding: utf-8 -*-

import array
import collections


G_INF = 2 ** 31


class GraphError(Exception):
    pass


class GraphSearchError(GraphError):

    def __init__(self, reason):
        self.reason = reason

    def __str__(self):
        return str(reason)


class ShortestPathFasterAlgorithm(object):

    def __init__(self, number_of_vertices, adjacency_list, costs, start):
        self.max_v = number_of_vertices
        self.adj = adjacency_list
        self.costs = costs
        self.start = start
        self.dist = None
        self.visits = None

    def initialize(self):
        self.dist = collections.defaultdict(lambda: G_INF)
        self.dist[self.start] = 0
        self.visits = collections.defaultdict(int)

    def single_source_shortest_path(self):
        self.initialize()
        q = collections.deque()
        q.append(self.start)
        while q:
            u = q.popleft()
            self.visits[u] += 1
            if self.visits[u] >= self.max_v:
                if self.max_v == 1:
                    return [0]
                raise GraphSearchError("A negative cycle was detected.")
            for v in self.adj[u]:
                new_length = self.dist[u] + self.costs[(u, v)]
                if new_length < self.dist[v]:
                    self.dist[v] = new_length
                    if v not in q:
                        q.append(v)
        return self.dist


def main():
    max_v, max_e, start = map(int, input().split())
    adjacency_list = collections.defaultdict(lambda: array.array("L"))
    costs = collections.defaultdict(lambda: G_INF)
    for _ in range(max_e):
        s, t, d = map(int, input().split())
        adjacency_list[s].append(t)
        costs[(s, t)] = d
    spfa = ShortestPathFasterAlgorithm(max_v, adjacency_list, costs, start)
    try:
        dist = spfa.single_source_shortest_path()
        for v in range(max_v):
            result = dist[v]
            if result < G_INF:
                print(result)
            else:
                print("INF")
    except GraphSearchError as gse:
        print("NEGATIVE CYCLE")


if __name__ == '__main__':
    main()