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 <bits/stdc++.h>
using namespace std;
struct edge{
	int u,v,w;
}e[2005];
int d[2005];
int inf=100000000;
int f[2005];
int find(int x){return f[x]==x?x:f[x]=find(f[x]);}
void join(int x,int y){
	int fx=find(x);
	int fy=find(y);
	if(fx==fy)return;
	f[fx]=fy;
}
int main(){
	int n,m,s,u,v,w;cin>>n>>m>>s;
	for(int i=0;i<m;i++)cin>>u>>v>>w,e[i]={u,v,w};
	for(int i=0;i<=n;i++)d[i]=inf,f[i]=i;
	bool ok=1;d[s]=0;
	for(int i=0;i<n;i++){
		bool change=0;
		for(int j=0;j<m;j++)
			if(d[e[j].u]+e[j].w<d[e[j].v])
				d[e[j].v]=d[e[j].u]+e[j].w,change=1,join(e[j].v,e[j].u);
	}
	for(int j=0;j<m;j++)
		if(d[e[j].u]+e[j].w<d[e[j].v])
			if(find(e[j].u)==find(s))ok=0;
	if(!ok){cout<<"NEGATIVE CYCLE"<<endl;return 0;}
	for(int i=0;i<n;i++)if(find(i)!=find(s)||d[i]>=inf-1000*10000)cout<<"INF"<<endl;else cout<<d[i]<<endl;
	return 0;
}