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>
#define MAX INT_MAX
using namespace std;
int main(void)
{
	int v,e,r;
	int s[2000],t[2000],d[2000];
	
	int i,j;
	int length[2000];
 	bool flg;
	
	cin>>v>>e>>r;
	
	for(i=0;i<e;i++)	cin>>s[i]>>t[i]>>d[i];
	for(i=0;i<v;i++)	length[i]=MAX;
	
	length[r]=0;
	
	for(i=0;i<=v;i++){
			flg=false;
			for(j=0;j<e;j++){
				if(length[s[j]]!=MAX&&length[t[j]]>length[s[j]]+d[j]){
					length[t[j]]=length[s[j]]+d[j];
					flg=true;
				}
			}
			if(!flg)	break;
	}
	if(i>v&&flg) cout<<"NEGATIVE CYCLE"<<endl;
	else{
		for(i=0;i<v;i++){
			if(length[i]==MAX){
				cout<<"INF"<<endl;
			}
			else{
				cout<<length[i]<<endl;
			}
		}
	}
	return 0;
}