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 <algorithm>
#include <iostream>
#include <vector>
#include <string.h>
#include <math.h>
#include <time.h>
#include <stdlib.h>
#include <queue>

#define INF 214748364

using namespace std;

struct edge { int from,to,cost;};

int main(){
	int V,E,r,
	    s,t,d,
	    score[1000];
	vector<edge> G;
	bool nl=true;
	
	scanf("%d %d %d",&V,&E,&r);
	for(int i=0;i<E;i++){
		scanf("%d %d %d",&s,&t,&d);
		G.push_back( {s,t,d} );
	}
	
	fill(score , score + V , INF);
	score[r] = 0;
	
	for(int i=0;i<V;i++){
		for(int j=0;j<E;j++){
			edge e = G[j];
			if(score[e.from] != INF && score[e.to] > score[e.from]+e.cost){
				score[e.to] = score[e.from]+e.cost;
				if(i == V-1) nl=false;
			}
		}
	}
	
	if(nl){
		for(int i=0;i<V;i++){
			if(score[i]==214748364) printf("INF\n");
			else printf("%d\n",score[i]);
		}
	}
	else printf("NEGATIVE CYCLE\n");
		
	return 0;
}