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 INF=1e9;
int e,v,r;
int to[100000],from[100000],w[1000000],d[1000000];
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 1;
	}
	return 0;
}
int main(){
	cin>>v>>e>>r;
	fill(d,d+v,INF);
	for(int i=0;i<e;i++){
		cin>>from[i]>>to[i]>>w[i];
	}
	d[r]=0;
	for(int i=0;i<v;i++){
		for(int j=0;j<e;j++){
			bool o=relax(j);
			if(i==v-1 && o==true){
				cout<<"NEGATIVE CYCLE"<<endl;
				return 0;
			}
		}
	}
	for(int i=0;i<v;i++){
		if(d[i]!=INF){
			cout<<d[i]<<endl;
		}
		else{
			cout<<"INF"<<endl;
		}
	}
}