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++)
#define ALL(v) (v).begin(),(v).end()
#define int long long
using namespace std;
typedef vector<int>   vint;
typedef pair<int,int> pint;

const int MAX_V=1000;
const int INF=1e18;
struct edge{ int to,cost; };

int V,E,dist[MAX_V];
vector<edge> G[MAX_V];

bool bellman_ford(int s)
{   
    REP(i,V) dist[i]=INF;
    dist[s]=0;

    REP(cnt,V) REP(i,V){
        if(dist[i]==INF) continue;
        for(edge e:G[i]){
            if(dist[e.to]>dist[i]+e.cost){
                dist[e.to]=dist[i]+e.cost;
                if(cnt==V-1) return true;
            }
        }
    }
    return false;
}

signed main()
{   
    int r; cin>>V>>E>>r;
    REP(i,E){
        int a,b,c; cin>>a>>b>>c;
        G[a].push_back((edge){b,c});
    }
    if(bellman_ford(r))
        cout<<"NEGATIVE CYCLE"<<endl;
    else{
        REP(i,V){
            if(dist[i]==INF) cout<<"INF"<<endl;
            else cout<<dist[i]<<endl;
        }
    }
}