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 <stdio.h>
#include<vector>
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)
int main(void){
    int V,E,R;
    scanf("%d %d %d",&V,&E,&R);
    int s[2005],t[2005],d[2005];
    rep(i,E){
        scanf("%d %d %d",&s[i],&t[i],&d[i]);
    }
    //Bellman-Ford
    int map[1005];
    rep(i,V){map[i]=1111111111;}
    map[R]=0;
    rep(i,V){
        bool end=true;
        rep(j,E){
            if(map[s[j]]!=1111111111&&map[t[j]]>map[s[j]]+d[j]){
                if(i>=V-1){
                    printf("NEGATIVE CYCLE\n");
                    return 0;
                }else{
                    map[t[j]]=map[s[j]]+d[j];
                    end=false;
                }
            }
        }
        if(end)break;
    }
    rep(i,V){
        if(map[i]!=1111111111)printf("%d\n",map[i]);
        else printf("INF\n");
    }
    return 0;
    
}