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;
long long INF = 1e18;

struct Edge{
    int from;
    int to;
    int cost;
};

int main(){
    int v,e,r;
    cin>>v>>e>>r;

    Edge g[e+100];
    long long d[v+100];

    for(int i=0; i<e; i++){
        cin>>g[i].from>>g[i].to>>g[i].cost;
    }
    for(int i=0; i<v; i++){
        d[i]=INF;
    }

    d[r] = 0;
    bool update = true;
    long long cnt = 0;

     while(update){
         
        update = false;

        for(int i = 0; i < e; i++){

            Edge e = g[i];
            if(d[e.from] != INF && d[e.to] > d[e.from] + e.cost){

                d[e.to] = d[e.from] + e.cost;

                update = true;

            }

        }

        if(!update) break;
         cnt++;
         if(cnt==v){
             cout<<"NEGATIVE CYCLE"<<endl;
             return 0;
         }

    }

    for(int i=0; i<v ;i++){
        if(d[i]==INF){
            cout<<"INF"<<endl;
        }else{
            cout<<d[i]<<endl;
        }
    }

    return 0;

}