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>
#include<algorithm>

using namespace std;

const int MAXN = 2005, INF = 1e9;
int d[MAXN], x[MAXN], y[MAXN], w[MAXN];
int n, m, r;

bool bellman_ford(int r)
{
	fill(d, d + n, INF);
	d[r] = 0;
	for(int i = 0; i < n; i++)
		for(int j = 0; j < m; j++)
			d[y[j]] = min(d[y[j]], d[x[j]] + w[j]);
	for(int j = 0; j < m; j++)
		if(d[y[j]] > d[x[j]] + w[j] && d[y[j]] < INF / 10)
			return true;
	return false;
}

int main()
{
	cin >> n >> m >> r;
	for(int i = 0; i < m; i++)
		cin >> x[i] >> y[i] >> w[i];
	if(bellman_ford(r))
		cout << "NEGATIVE CYCLE" << endl;
	else
		for(int i = 0; i < n; i++)
			if(d[i] > INF / 10)
				cout << "INF" << endl;
			else
				cout << d[i] << endl;
	return 0;
}