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<climits>
using namespace std;

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

    int s[e], t[e], d[e];
    for(int i = 0; i < e; i++)  cin >> s[i] >> t[i] >> d[i];

    int dist[v];
    for(int i = 0; i < v; i++)  dist[i] = INT_MAX;
    dist[r] = 0;

    for(int i = 0; i < v-1; i++){
        for(int k = 0; k < e; k++){
            if(dist[s[k]] != INT_MAX)   
                dist[t[k]] = min(dist[t[k]], dist[s[k]] + d[k]);
        }
    }

    bool update = false;
    for(int k = 0; k < e; k++){
        if(dist[s[k]] == INT_MAX)   continue;
        if(dist[s[k]] + d[k] < dist[t[k]])  update = true;
    }
    
    if(update){
        cout << "NEGATIVE CYCLE" << endl;
    }else{
        for(int i = 0; i < v; i++){
            if(dist[i] == INT_MAX)  cout << "INF" << endl;
            else                    cout << dist[i] << endl;
        }
    }
    
    return 0;
}