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 from,to,cost;};

int n,m,s;
vector<edge>v;
int d[100009];

void Bellman(){
	fill(d,d+100009,1e9);
	d[s]=0;
	for(int i=0;i<n;i++){
		int update=0;
		for(int j=0;j<m;j++){
			edge e=v[j];
			if(d[e.from]!=1e9&&d[e.to]>d[e.from]+e.cost){
				d[e.to]=d[e.from]+e.cost;
				update=1;
				if(i==n-1){
					cout<<"NEGATIVE CYCLE"<<endl;
					return;
				}
			}
		}
		if(!update)break;
	}
	for(int i=0;i<n;i++){
		if(d[i]==1e9)cout<<"INF"<<endl;
		else cout<<d[i]<<endl;
	}
}
int main(){
	cin>>n>>m>>s;
	for(int i=0;i<m;i++){
		int a,b,c;
		cin>>a>>b>>c;
		v.push_back({a,b,c});
	}
	Bellman();
}