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<cstdio>
#include<functional>
#include<algorithm>
#define MM 2100000000
using namespace std;
int main(void)
{
	int v,e,r,s[2000],t[2000],d[2000],leng[1000],i,j,flg;
	scanf("%d %d %d",&v,&e,&r);
	for(i=0;i<e;i++)	scanf("%d %d %d",&s[i],&t[i],&d[i]);
	for(i=0;i<v;i++)	leng[i]=MM;
	leng[r]=0;
	for(i=0;i<=v;i++)	{
		flg=0;
		for(j=0;j<e;j++)	{
			if(leng[s[j]]!=MM && leng[s[j]]+d[j]<leng[t[j]])	{
				leng[t[j]]=leng[s[j]]+d[j];
				flg=1;
			}
		}
		if(flg==0)	break;
	}
	if(i>v && flg==1)	{
		printf("NEGATIVE CYCLE\n");
	}
	else {
		for(i=0;i<v;i++)	{
			if(leng[i]==MM)	printf("INF\n");
			else printf("%d\n",leng[i]);
		}
	}
	return 0;
}