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 rep(i,n) for(int i=0; i<n;i++)
using namespace std;
using ll = long long;
#define int ll

signed  main(){
    using pii =pair<int,int>;
    using piii=pair<pii,int>;
    int v,e,s; cin>>v>>e>>s;
    vector<int>d(v,LLONG_MAX);
    vector<piii>edge;
    rep(i,e){
        int from,to,cost; cin>>from>>to>>cost;
        edge.push_back(piii(pii(from,to),cost));
    }
    d[s]=0;
    rep(i,v){
        bool update=false;
        rep(j,edge.size()){
            int to=edge[j].first.second;
            int from=edge[j].first.first;
            int cost=edge[j].second;
            if(d[from]==LLONG_MAX)continue;
            if(d[to]>d[from]+cost){
                d[to]=d[from]+cost;
                update=true;
            }
        }
        if(i==v-1&&update)return puts("NEGATIVE CYCLE")*0;
    }
    rep(i,v)if(d[i]!=LLONG_MAX)cout<<d[i]<<endl; else cout<<"INF"<<endl;
}