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>
#define rep(i, n) for (int i = 0; i < (n); i++)
using namespace std;
using ll = long long;
using P = pair<int, int>;
const int INF = numeric_limits<int>::max();

struct edge {
    int from, to, cost;
};

struct Graph {
    vector<edge> es;
    vector<int> d;
    Graph(int n) {
        d.assign(n, INF);
    }
};

int main()
{
    int nv, ne, r;
    cin >> nv >> ne >> r;
    Graph g(nv);
    rep(i, ne) {
        int s, t, d;
        cin >> s >> t >> d;
        g.es.push_back({s, t, d});
    }
    g.d[r] = 0;
    rep(i, nv) {
        for (auto& e : g.es) {
            if (g.d[e.from] != INF && g.d[e.to] > g.d[e.from] + e.cost) {
                if (i == nv - 1) {
                    cout << "NEGATIVE CYCLE" << endl;
                    return 0;
                }
                g.d[e.to] = g.d[e.from] + e.cost;
            }
        }
    }
    for (auto d : g.d) {
        if (d == INF) {
            cout << "INF" << endl;
        } else {
            cout << d << endl;
        }
    }
}