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;

struct Edge { int from, to, cost; };
const int INF = 1 << 17;
const int V = 1001;
const int E = 2001;
int d[V];
Edge edge[E];

int main()
{
	cin.tie(0);
	ios::sync_with_stdio(false);
	
	int v, e, r;
	cin >> v >> e >> r;
	
	int a, b, c;
	for(int i = 0; i < e; ++i){
		cin >> a >> b >> c;
		edge[i] = Edge{ a, b, c };
	}
	
	fill(d, d + v, INF);
	d[r] = 0;
	
	int cnt = 0;
	while(true){
		bool update = false;
		for(int i = 0; i < e; ++i){
			Edge e1 = edge[i];
			if(d[e1.from] != INF && d[e1.to] > d[e1.from] + e1.cost){
				d[e1.to] = d[e1.from] + e1.cost;
				update = true;
			}
		}
		cnt ++;
		if(!update)
			break;
		if(cnt == v - 1){
			cout << "NEGATIVE CYCLE" << endl;
			return 0;
		}
	}
	
	for(int i = 0; i < v; ++i){
		if(d[i] == INF)
			cout << "INF";
		else
			cout << d[i];
		cout << endl;
	}
	
	return 0;
}