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;

const int INF = 1<<30;

typedef struct{
    int s, t, d;
}Edge;

int V, E, R;

bool bellman_ford(vector<Edge> &edges, int s, vector<int> &d){
    d[s] = 0;
    
    bool updated = true;
    for(int i=0; i<V; i++){
        updated = false;
        for(auto edge: edges){
            if(d[edge.s] != INF && d[edge.t] > d[edge.s] + edge.d){
               d[edge.t] = d[edge.s] + edge.d;
                updated = true;
            }
        }
    }
    return updated;
}

int main(){
    cin >> V >> E >> R;
    vector<Edge> edges;
    for(int i=0; i<E; i++){
        int s, t, d;
        cin >> s >> t >> d;
        edges.push_back({s, t, d});
    }
    
    vector<int> d(V, INF);
    bool neg_loop = bellman_ford(edges, R, d);
    
    if(neg_loop){
        cout << "NEGATIVE CYCLE" << endl;
    }else{
        for(auto v: d){
            if(v == INF)
                cout << "INF" << endl;
            else
                cout << v << endl;
        }
    }
    
    return 0;
}