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 1000000007
typedef long long ll;
struct Edge{ll u,v,cost;};
using Edges = vector<Edge>;

vector<ll> Bellman_ford(const Edges &edges,int V,int s){
    vector<ll> dist(V,INF);
    dist[s] = 0;
    for(int i = 0; i < V ; i++){
        for(auto e : edges){
            if(dist[e.u] == INF)continue;
            if(dist[e.v] > dist[e.u]+e.cost){
                dist[e.v] = dist[e.u]+e.cost;
                if(i == V-1)return vector<ll>();
            }
        }
    }
    return dist;
}

int main(){
    int V,E,s;cin >> V >> E >> s;
    Edges es(E);
    for(int i = 0; i < E ; i++){
        cin >> es[i].u >> es[i].v >> es[i].cost;
    }

    vector<ll> dist = Bellman_ford(es,V,s);
    if(dist.empty())cout << "NEGATIVE CYCLE" << endl;
    else{
        for(auto d : dist){
            if(d == INF)cout << "INF" << endl;
            else cout << d << endl;
        }
    }

    return 0;
}