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 <iostream>
using namespace std;

struct edge {
	int s, t, d;
};

int v, e, r, ct = 0;
edge es[2000];
long d[1000];
const long Mx = 0xFFFFFFF;

int main()
{
	cin >> v >> e >> r;

	for (int i = 0; i < e; i++)
		cin >> es[i].s >> es[i].t >> es[i].d;

	for (int i = 0; i < v; i++)
		d[i] = Mx;

	d[r] = 0;

	while (true) {
		bool f = true;
		for (int i = 0; i < v; i++) {
			for (int j = 0; j < e; j++) {
				edge e = es[j];
				if (d[e.s] != Mx && d[e.t] > d[e.s] + e.d) {
					d[e.t] = d[e.s] + e.d;
					f = false;
				}
			}
		}
		ct++;
		if (ct > v || f)
			break;
	}

	if (ct > v)
		cout << "NEGATIVE CYCLE" << endl;
	else {
		for (int i = 0; i < v; i++) {
			if (d[i] == Mx)
				cout << "INF" << endl;
			else
				cout << d[i] << endl;
		}
	}

	return 0;
}