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<stdio.h>
#include<algorithm>
#include<iostream>
#include<vector>
#include<queue>
#define REP(i,n) for(long long int (i)=0;(i) < (n);(i)++)
#define MAX_V 1001
#define MAX_E 2001
#define INF (1e9 + 1)

using namespace std;

struct edge{
  int from,to,cost;
};
vector<edge> edges;

int V,E,r,a,b,c;
int d[MAX_V];

void bellford(){
  REP(i,MAX_V) d[i] = INF;
  d[r] = 0;
  REP(i,V){
    bool update = false;
    REP(j,E){
      edge e = edges[j];
      if(d[e.from] != INF && d[e.from]+e.cost < d[e.to]){
        update = true;
        d[e.to] = d[e.from]+e.cost;
        if(i==V-1){
          cout << "NEGATIVE CYCLE" << endl;
          return;
        }
      }
    }
    if(!update)break;
    }

    REP(i,V){
      if(d[i]==INF)cout << "INF"<<endl;
      else cout << d[i] << endl;
    }
}


int main(){
  scanf("%d %d %d",&V,&E,&r);
  REP(i,E){
    scanf("%d %d %d",&a,&b,&c);
    edges.push_back((edge){a,b,c});
  }
  bellford();
}