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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

int	main()
{
	const static int	inf = 2000 * 10000 + 1;
	int	V, E, r;
	cin >> V >> E >> r;
	vector<int>	v_cost(V, inf);
	map<int, map<int, int>>	e_cost;
	int	s, t, d;
	for (int i = 0; i < E; ++i) {
		cin >> s >> t >> d;
		if (!e_cost.count(s))
			e_cost[s] = map<int, int>();
		e_cost.at(s)[t] = d;
	}
	bool	updated = false;
	v_cost.at(r) = 0;
	int		tmp_cost;
	for (int i = 0; i < V; ++i) {
		updated = false;
		for (s = 0; s < V; ++s) {
			if (v_cost.at(s) == inf)
				continue;
			if (!e_cost.count(s))
				continue;
			for (auto pr : e_cost.at(s)) {
				t = pr.first;
				tmp_cost = pr.second + v_cost.at(s);
				if (tmp_cost < v_cost.at(t)) {
				   v_cost.at(t) = tmp_cost;
				   updated = true;
				}
			}
		}
		if (!updated)
			break;
	}
	if (updated) {
		cout << "NEGATIVE CYCLE" << endl;
		return 0;
	}
	for (int i = 0; i < V; ++i) {
		if (v_cost.at(i) == inf)
			cout << "INF" << endl;
		else
			cout << v_cost.at(i) << endl;
	}
}