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 be(v) (v).begin(),(v).end()
#define pb(q) push_back(q)
typedef long long ll;
using namespace std;
const ll mod=1000000007;
#define doublecout(a) cout<<fixed<<setprecision(10)<<a<<endl;
struct edge{ll from,to,cost;};
int main() {
    cin.tie(0);
    cout.tie(0);
    ios::sync_with_stdio(false);
    ll n,m,a,b,c,r;
    cin>>n>>m>>r;
    ll d[n];
    bool maki;
    vector<edge> g;
    for(int i=0;i<n;i++)d[i]=mod*mod;
    d[r]=0;
    for(int i=0;i<m;i++){
        cin>>a>>b>>c;
        g.push_back({a,b,c});
    }
    for(int i=0;i<n*2;i++){
    	maki=false;
        for(int j=0;j<m;j++){
            if(d[g[j].from]!=mod*mod&&d[g[j].to]>d[g[j].from]+g[j].cost){
                d[g[j].to]=d[g[j].from]+g[j].cost;
                maki=true;
            }
        }
    }
    if(maki){
    	cout << "NEGATIVE CYCLE" <<endl;
    	return 0;
    }
    for(int i=0;i<n;i++){
    	if(d[i]==mod*mod){
    		cout << "INF" <<endl;
    	}else{
    		cout << d[i] <<endl;
    	}
    }
    return 0;
}