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;

#define rep(i,n) for(i = 0;i < n;++i)
#define all(v) v.begin(), v.end()
using ll = long long;

int main()
{
    ll i,j;
    ll INF = 1e18;
    
    ll v,e,r;
    cin >> v >> e >> r;

    vector<ll> s(e);
    vector<ll> t(e);
    vector<ll> d(e);
    for(i = 0;i < e;++i){
        cin >> s.at(i) >> t.at(i) >> d.at(i);
    }
    
    vector<ll> vdist(v,INF);
    ll top = r;
    vdist.at(top) = 0;
    rep(j, v){
        bool update = false;
        for(i = 0;i < e;++i){
            if(vdist.at(s.at(i)) != INF && vdist.at(t.at(i)) > vdist.at(s.at(i)) + d.at(i)){
                vdist.at(t.at(i)) = vdist.at(s.at(i)) + d.at(i);
                update = true;
            }
        }
        if(!update) break;
        else if(j == v-1){
            cout << "NEGATIVE CYCLE" << endl;
            return 0;
        }
    }
    

    for(i = 0;i < v;++i){
        if(vdist.at(i) >= 1e14) cout << "INF" << endl;
        else cout << vdist.at(i) << endl;
    }

    return 0;
}