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;
typedef pair<int,int> PA;
#define to first
#define cost second
int main(){
  int v,e,r,a,b,c;
  vector<PA> vec[2000];
  scanf("%d %d %d",&v,&e,&r);
  for(int i=0;i<e;i++){
    scanf("%d %d %d",&a,&b,&c);
    vec[a].push_back(PA(b,c));
  }
  int min_cost[1000];
  fill(min_cost,min_cost+1000,INT_MAX);
  min_cost[r] = 0;
  for(int i=0;i<e;i++){
    for(int j=0;j<e;j++){
      for(int k=0;k<vec[j].size();k++){
	PA d = vec[j][k];
	if(min_cost[j] == INT_MAX || min_cost[d.to] <= min_cost[j]+d.cost) continue;
	min_cost[d.to] = min_cost[j]+d.cost;
	if(i == e-1){
	  puts("NEGATIVE CYCLE");
	  return (0);
	}
      }
    }
  }
  for(int i=0;i<v;i++){
    if(min_cost[i] == INT_MAX) puts("INF");
    else printf("%d\n",min_cost[i]);
  }
  return (0);
}