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;

struct edge{int to,cost;};

int N,M,r;
vector<edge>G[1000];

int main(){
    cin>>N>>M>>r;
    for(int i=0;i<M;i++){
        int s,t,d;
        cin>>s>>t>>d;
        G[s].push_back((edge){t,d});
    }

    int dist[1000];
    fill_n(dist,N,1e9);
    dist[r]=0;
    for(int i=0;;i++){
        bool update=false;
        for(int j=0;j<N;j++)if(dist[j]!=1e9)for(int k=0;k<G[j].size();k++){
            edge &e=G[j][k];
            if(dist[e.to]>dist[j]+e.cost){
                update=true;
                dist[e.to]=dist[j]+e.cost;
            }
        }

        if(!update)break;
        if(i>=N){
            cout<<"NEGATIVE CYCLE"<<endl;
            return 0;
        }

    }

    for(int i=0;i<N;i++){
        if(dist[i]==1e9)cout<<"INF"<<endl;
        else cout<<dist[i]<<endl;
    }

    return 0;
}