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 _GLIBCXX_DEBUG
#define rep(i,n) for(long long i = 0; i < (n); ++i)
#define ll long long
#define P pair<ll,ll>
#define all(v) (v).begin(),(v).end()

const ll mod = 1e9+7;
const ll INF = 1e18;
const double pi = acos(-1.0);

int main(void)
{
    struct edge{
        ll from;
        ll to;
        ll cost;
    };

    ll v,e,r;
    cin>>v>>e>>r;
    vector<edge> E(e);
    rep(i,e){
        ll s,t,d;
        cin>>s>>t>>d;
        E[i]={s,t,d};
    }

    vector<ll> dist(v,INF);
    dist[r]=0;
    rep(i,v){
        bool update=false;
        for(auto x:E){
            if(dist[x.from] != INF && dist[x.from]+x.cost < dist[x.to]){
                if(i==v-1){
                    cout<<"NEGATIVE CYCLE"<<endl;
                    return 0;
                }
                dist[x.to] = dist[x.from]+x.cost;
                update=true;
            }
        }
        if(!update) break;
    }
    rep(i,v){
        if(dist[i]==INF) cout<<"INF"<<endl;
        else cout<<dist[i]<<endl;
    }
    return 0;
}