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 ll = long long;
using namespace std;

using Weight = int;

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

using Edges = std::vector<edge>;
using Graph = std::vector<Edges>;

const Weight winf = numeric_limits<Weight>::max();

vector<Weight> bellman_ford(const Edges& es, int V, int s)
{
    vector<Weight> dst(V, winf);
    dst[s] = 0;

    for (int i = 0; i < V; i++) {
        for (auto& e: es) {
            if (dst[e.from] != winf && dst[e.to] > dst[e.from] + e.weight) {
                dst[e.to] = dst[e.from] + e.weight;
                if (i == V - 1) return vector<Weight> ();
            }
        }
    }
    return dst;
}

int main()
{
    int v, e, r; cin >> v >> e >> r;
    Edges es;
    for (int i = 0; i < e; i++) {
        int s, t, d; cin >> s >> t >> d;
        es.push_back({s, t, d});
    }

    auto bf = bellman_ford(es, v, r);
    if (bf.empty()) cout << "NEGATIVE CYCLE" << endl;
    else {
        for (int i = 0; i < v; i++) {
            cout << (bf[i] == winf ? "INF" : to_string(bf[i])) << endl;
        }
    }
    return 0;
}