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;

#define INF INT_MAX
#define FF first.first
#define FS first.second
#define S second
typedef pair<int,int> P;
typedef pair<P,int> PP;

int main(void)
{
	int v,e,r;
	int s,t,d;
	int i,j;
	int leng[1000];
	int flg=0;
	int cnt=0;
	PP p[2000];
	
	cin>>v>>e>>r;
	for(i=0;i<e;i++){
		cin>>s>>t>>d;
		p[i] = PP(P(s,t),d);
	}
	
	//cout<<p[0].FF<<" "<<p[0].FS<<" "<<p[0].S<<endl;
	
	for(i=0;i<v;i++) leng[i]=INF;
	leng[r]=0;
	while(1){
		bool updete=false;
		for(i=0;i<e;i++){
			if(leng[p[i].FF]!=INF&&leng[p[i].FS]>leng[p[i].FF]+p[i].S){
				leng[p[i].FS]=leng[p[i].FF]+p[i].S;
				updete=true;
			}
		}
		if(!updete) break;
		if(cnt==v-1){
			flg=1;
			break;
		}
		cnt++;
	}
	
	for(i=0;i<v;i++){
		if(flg==1){
			cout<<"NEGATIVE CYCLE"<<endl;
			break;
		}
		else if(leng[i]==INF) cout<<"INF"<<endl;
		else cout<<leng[i]<<endl;
	}
		
	return 0;
}