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;
typedef long long ll;
#define all(x) (x).begin(),(x).end()
const int mod=1000000007,MAX=1001;
const ll INF=1LL<<60;

vector<pair<int,ll>> S[MAX];
ll dis[MAX];
int N;

bool bell(int u){
    for(int i=0;i<N;i++){
        dis[i]=INF;
    }
    dis[u]=0;

    for(int k=0;k<N;k++){
        for(int i=0;i<N;i++){
            for(int j=0;j<S[i].size();j++){
                int a=S[i][j].first;
                ll b=S[i][j].second;
                if(dis[i]!=INF&&dis[a]>dis[i]+b){
                    dis[a]=dis[i]+b;
                    if(k==N-1) return true;
                }
            }
        }
    }

    return false;

}

int main(){
    
    int E,r;cin>>N>>E>>r;
    for(int i=0;i<E;i++){
        int a,b;
        ll c;cin>>a>>b>>c;
        S[a].push_back(make_pair(b,c));
    }

    if(bell(r)) cout<<"NEGATIVE CYCLE"<<endl;
    else{
        for(int i=0;i<N;i++){
            if(dis[i]!=INF) cout<<dis[i]<<endl;
            else cout<<"INF"<<endl;
        }
    }
}