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:
//ITNOA
#include<iostream>
#include<cstdio>
using namespace std;
#define F first
#define S second
typedef long long ll;
const ll INF=1e18,MAX=3000,MOD=1e9+7;
typedef pair<ll,ll> pii;
typedef pair<pii,ll> piii;
piii e[MAX];
ll d[MAX];
bool relax(int v){
	if(d[e[v].F.F]+e[v].S<d[e[v].F.S]&&d[e[v].F.F]!=INF){
		d[e[v].F.S]=d[e[v].F.F]+e[v].S;
		return 1;
	}
	return 0;
}
int main(){
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	int n,m,s;
	cin>>n>>m>>s;
	for(int i=0;i<m;i++)
		cin>>e[i].F.F>>e[i].F.S>>e[i].S;
	fill(d,d+n,INF);
	d[s]=0;
	for(int i=0;i<n-1;i++){
		for(int j=0;j<m;j++)
			relax(j);
	}
	bool t=0;
	for(int i=0;i<m;i++){
		if(relax(i))
			t=1;
	}
	if(t)	
		cout<<"NEGATIVE CYCLE\n";
	else{
		for(int i=0;i<=n-1;i++){
			if(d[i]==INF)
				cout<<"INF\n";
			else
				cout<<d[i]<<"\n";
		}
	}
	return 0;
}