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<cstdio>
	#include<vector>
	using namespace std;
	const int MAX_N=100000+100;
	long long int INF=2e10;
	vector<int> w,from,to;
	long long d[MAX_N];
	bool ans=false;
	bool relax(int e){
		if(d[to[e]]>d[from[e]]+w[e] && d[from[e]]!=INF){
			d[to[e]]=d[from[e]]+w[e];
			return true;
		}
		return false;
	}
	int main(){
		int n,m,s,a,b,c;
		cin>>n>>m>>s;
		fill(d,d+n+10,INF);
		d[s]=0;
		for(int i=0;i<m;i++){
			cin>>a>>b>>c;
			from.push_back(a);
			to.push_back(b);
			w.push_back(c);
		}
		for(int i=0;i<n;i++){
			ans=false;
			for(int j=0;j<m;j++){
				if(relax(j)==true){
					ans=true;
				}
			}
		}
		if(ans==true){
			cout<<"NEGATIVE CYCLE"<<endl;
			return 0;
		}
		for(int i=0;i<n;i++){
			if(d[i]==INF){
				cout<<"INF"<<endl;
			}
			else
				cout<<d[i]<<endl;
		}
	}