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 <algorithm>
#include <iostream>
#include <vector>
#include <queue>
using namespace std;
typedef pair<long long int,int> P;
struct vertex{
    vector<P> E;//cost,to
};
#define INF 5000000001
vertex V[100000];
long long int minimum[100000];

int main(){
    int NV,NE,r;
    cin>>NV>>NE>>r;
    fill(minimum,minimum+100000,INF);
    minimum[r]=0;
    for(int i=0;i<NE;i++){
        int s,t,d;
        cin>>s>>t>>d;
        V[s].E.emplace_back(d,t);
    }
    bool update;
    for(int i=0;i<NV;i++){
        update=false;
        for(int j=0;j<NV;j++){
            if(minimum[j]==INF) continue;
            for(auto& e:V[j].E){
                int to=e.second, cost=e.first;
                if(minimum[j]+cost<minimum[to]){
                    minimum[to]=minimum[j]+cost;
                    update=true;
                }
            }
        }
    }
    if(update){
        cout<<"NEGATIVE CYCLE"<<endl;
        return 0;
    }
    for(int i=0;i<NV;i++){
        if(minimum[i]==INF){
            cout<<"INF"<<endl;
        }else{
            cout<<minimum[i]<<endl;
        }
    }
    return 0;
}