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>
#include<string>
using namespace std;

struct edge{int to,cost;};
vector<edge> G[100010];
vector<int> node;
const int INF = 1e9;
int V,E,r;

bool Bellman_Ford(int r){
    node = vector<int>(V,INF);
    node[r] = 0;
    for(int i=0;i<V;++i){
        for(int v=0;v<V;++v){
            for(auto e: G[v]){
                if(node[v] == INF) continue;
                if(node[e.to] > node[v] + e.cost){
                    node[e.to] = node[v] + e.cost;
                    if(i == V-1) return true;
                }
            }
        }
    }
    return false;
}

int main(){
    cin >> V >> E >> r;
    for(int i = 0;i<E;++i){
        int s,t,c;
        cin >> s >> t >> c;
        G[s].push_back({t,c});
    }

    bool negloop = Bellman_Ford(r);

    if(negloop){
        cout << "NEGATIVE CYCLE" << endl;
        return 0;
    }
    for(auto e : node){
        if(e == INF) cout << "INF" << endl;
        else cout << e << endl;
    }
}