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 <algorithm>
#include <string>
#include <queue>
#include <vector>
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
struct edge{int from, to, cost;};
#define INF 1000000001

int V,E,d[1005];
edge es[2005];

bool find_negative_loop(int s){
	int cnt=0;
	for(int i=0;i<V;i++)d[i]=INF;
	d[s]=0;
	while(1){
		bool update=false;
		cnt++;
		for(int i=0;i<E;i++){
			edge e=es[i];
			if(d[e.from]!=INF&&d[e.to]>d[e.from]+e.cost){
				d[e.to]=d[e.from]+e.cost;
				if(cnt==V)return true;
				update=true;
			}
		}
		if(!update)break;
	}
	return false;
}

int main(void){
	int r;
	cin>>V>>E>>r;
	for(int i=0;i<E;i++){
		cin>>es[i].from>>es[i].to>>es[i].cost;
	}
	if(find_negative_loop(r)){
		cout<<"NEGATIVE CYCLE\n";
	}else{
		for(int i=0;i<V;i++){
			if(d[i]==INF)cout<<"INF\n";
			else cout<<d[i]<<endl;
		}
	}
	return 0;
}