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<vector>
#include<queue>
#include<climits>
using namespace std;

struct Edge{int s,t,cost;};

int main(){
	int V,E,r;
	cin >> V >> E >> r;
	
	vector<Edge> G(E);
	for (int i=0;i<E;i++){
		cin >> G[i].s >> G[i].t >> G[i].cost;
	}
	
	vector<int> d(V,INT_MAX);
	d[r]=0;
	
	for (int i=0;i<V;i++){
		for (int j=0;j<E;j++){
			Edge e=G[j];
			if(d[e.s]==INT_MAX){
				continue;
			}else{
				if(d[e.t]>d[e.s]+e.cost){
					d[e.t]=d[e.s]+e.cost;
				}
			}
		}
	}
	bool flag=0;
	for (int j=0;j<E;j++){
			Edge e=G[j];
			if(d[e.s]==INT_MAX){
				continue;
			}else{
				if(d[e.t]>d[e.s]+e.cost){
					flag=1;
					break;
				}
			}
		}
	
	if(flag){
		cout << "NEGATIVE CYCLE" <<endl;
	}else{
	for (int i=0;i<V;i++){
		if(d[i]==INT_MAX){
			cout << "INF" << endl;
		}else{
			cout << d[i] << endl;
		}
	}
	}
	return 0;
}