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 MAXN = 10000;
int n,m,src;
struct ed{
    int u,v,cost;
};
vector<ed> e;
long long  dis[MAXN];

void ballmanf(){
    memset(dis,63,sizeof dis);
    long long inf = dis[0];
    dis[src] = 0;
    bool nc = false;
    for(int i=0; i<n; i++){
        nc=false;
        for(int j=0; j<m; j++){
            if( dis[e[j].u] < inf){
                if(dis[e[j].v] > dis[e[j].u] + e[j].cost){
                nc=true;
                dis[e[j].v] = min(dis[e[j].v],dis[e[j].u]+e[j].cost);

                }
            }
        }
    }

    if(nc){
        cout<<"NEGATIVE CYCLE"<<"\n";
    }
    else{
        for(int i=0; i<n; i++){
            if(dis[i]==inf){
                cout<<"INF"<<"\n";
            }
            else{
                cout<<dis[i]<<"\n";
            }
        }
    }
}

int main() {
    // freopen("./input.txt","r",stdin);
    // freopen("./output.txt","w",stdout);

    ios::sync_with_stdio(false); cin.tie(nullptr);
    cin>>n>>m>>src;
    for(int i=0;i<m;i++){
        int a,b,c; cin>>a>>b>>c;
        e.push_back({a,b,c});
    }
    ballmanf();
}