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 long long ll;
struct edge{ll from;ll to;ll cost;};
const ll inf = 100100100100100100;
const ll MAX_V = 1000;
const ll MAX_E = 2000;
ll V,E,D[MAX_V];edge G[MAX_E];
bool BellmanFord(ll s){
    ll i,j;fill(D,D+V,inf);bool update;D[s] = 0;
    for(i=0;i<V;i++){
        update = false;
        for(j=0;j<E;j++){
            if(D[G[j].from] != inf && D[G[j].to] > D[G[j].from]+G[j].cost){
                D[G[j].to] = D[G[j].from]+G[j].cost;
                update = true;
            }
        }
        if(!update) return false;
    }
    return true;
}
int main(){
  ll r,i;scanf("%lld%lld%lld",&V,&E,&r);
  for(i=0;i<E;i++) scanf("%lld%lld%lld",&G[i].from,&G[i].to,&G[i].cost);
  if(BellmanFord(r)){
    printf("NEGATIVE CYCLE\n");return 0;
  }
  for(i=0;i<V;i++){
    if(D[i]==inf) printf("INF\n");
    else printf("%lld\n",D[i]);
  }
  return 0;
}