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 <iostream>
#include <vector>
#include <algorithm>
using namespace std;
typedef pair<int,int> pii;
typedef vector<int> vint;
const int inf=1e9;
int dist[1010];
int s[2010],t[2010],d[2010];
int main(){
    int v,e,r;  cin>>v>>e>>r;
    for(int i=0;i<v;i++)    dist[i]=inf;
    dist[r]=0;
    for(int i=0;i<e;i++)    cin>>s[i]>>t[i]>>d[i];
    int i=0;
    for(;i<v;i++){
        bool updated=false;
        for(int j=0;j<e;j++){
            if(dist[s[j]]==inf) continue;
            if(dist[t[j]]>dist[s[j]]+d[j]){
                updated=true;
                dist[t[j]]=dist[s[j]]+d[j];
            }
        }
        if(updated==false)   break;
    }
    if(i<v){
        for(int i=0;i<v;i++){
            if(dist[i]==inf)    cout<<"INF"<<endl;
            else    cout<<dist[i]<<endl;
        }
    }
    else    cout<<"NEGATIVE CYCLE"<<endl;
    return 0;
}