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 <vector>
#include <iostream>
#include <limits>

using namespace std;

struct edge {
    int from;
    int to;
    int weight;
};

int main() {
    const auto INF = numeric_limits<int>::max();

    int V, E, r;
    cin >> V >> E >> r;

    vector<edge> edges;
    for (int i = 0; i < E; ++i) {
        int s, t, d;
        cin >> s >> t >> d;

        edges.push_back(edge{s, t, d});
    }

    // Bellman-Ford algorithm
    vector<int> d(V, INF);
    d[r] = 0;
    for (auto i = 0; i < V; ++i) {
        for (auto& e : edges) {
            // cerr << ": " << e.from << " " << e.to << " " << e.weight << endl;
            if (d[e.from] != INF && d[e.from] + e.weight < d[e.to]) {
                d[e.to] = d[e.from] + e.weight;
            }
        }
    }
    for (auto& e : edges) {
        if (d[e.from] != INF && d[e.from] + e.weight < d[e.to]) {
            cout << "NEGATIVE CYCLE" << endl;
            return 0;
        }
    }

    for (auto x : d) {
        if (x == INF) {
            cout << "INF" << endl;
        } else {
            cout << x << endl;
        }
    }

    return 0;
}