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;
#define INF 1000000000
#define MAX_V 2000

int D[MAX_V][MAX_V];
int V,E,r;

void warshall_floyd(){
    int i,j,k;
    for(k=0;k<V;k++){
        for(i=0;i<V;i++){
            for(j=0;j<V;j++){
                D[i][j]=min(D[i][j],D[i][k]+D[k][j]);
            }
        }
    }
}

int main(){
    int i,j,s,t,d,dall=0;
    bool flg=false;
    cin>>V>>E>>r;
    for(i=0;i<V;i++){
        for(j=0;j<V;j++){
            if(i==j)D[i][j]=0;
            else D[i][j]=INF;
        }
    }
    for(i=0;i<E;i++){
        cin>>s>>t>>d;
        D[s][t]=d;
        if(d>=0)dall+=d;
    }

    warshall_floyd();
    /*for(i=0;i<V;i++){
        for(j=0;j<V;j++)cout<<D[i][j]<<" ";
        cout<<"\n";
    }*/

    for(i=0;i<V;i++){
        if(D[i][i]<0 && D[r][i]<=dall){
            flg=true;
            break;
        }
    }

    if(flg){
        cout<<"NEGATIVE CYCLE\n";
    }else{
        for(i=0;i<V;i++){
            if(D[r][i]>dall)cout<<"INF\n";
            else cout<<D[r][i]<<"\n";
        }
    }
}