We have a map for farming land in a country. The whole farming land of the country is divided into a set of disjoint farming regions. Each farmer owns only one farming region in this country. There is a boundary fence between two neighboring farming regions. The farmland map for this country can be represented in a plane graph. The following Figure-1 shows one example.

Figure-1: Farmland graph G(V,E)

There are two types of edges, boundary edge and non-boundary edge. All edges of G(V,E) except (v8, v6) and (v11, v10) are boundary edges which are between two neighboring farming regions. The "proper farming region" in a Farmland graph is a closed region bounded by a simple cycle and it should not contain any vertices or edges inside. In this figure, the polygon < v1,v9,v8,v7 >is a proper farming region, and the region < v2, v1, v7, v8 , v2, v5, v4, v3 >is not a proper farming region since its boundary cycle is not simple.

We assume that the farmland graph G(V,E) is a simple connected graph, which does not allow self-loops (Figure-2 (a)) and parallel edges (Figure-2 (b)).Also in Farmland graph G(V,E), we do not consider the outer face of G(V,E).You can see that there are 2 proper farming regions in G(V,E) shown in Figure-1,namely < v1,v9,v8,v7> and < v2,v3,v4,v5>, since there are no vertices or edges inside. But the polygon< v1,v7,v8,v2> is not a proper farming region since vertex v3, v4, and v5 are located in that region. Similarly, the region is not a proper region because a vertex v10 is inside the region.A degenerate polygon < v6, v8> is not a proper region because it has no valid area inside.

Figure-2: (a) self-loop < v1,v1> , and (b) 3 parallel edges { < v1,v2>,< v1,v2>, < v1,v2>}

There are other assumptions for input farmland graph data.

1. There is at least one proper farming region.

2. The position of each vertex in Farmland graph is distinct.

3. There is no edge crossing, which means the graph G(V,E) is a plane graph.

4. Farmland graph G(V,E) is simple and connected.

Let us define the "size" of proper farming region. The size of proper farming region is the number of boundary edges of that region. For example, the size of the proper farming region < v2,v3,v4,v5 > is 4.

The problem is to find the number of proper regions that have a specified size.If you are requested to find the number of proper regions with size of 4 in the graph given in Figure-1, you must answer that there are 2 proper regions whose sizes are 4 because farming regions < v1,v9,v8,v7 > and < v2,v3,v4,v5 >are proper regions and their sizes are 4. If there are no such regions, then you have to print 0.

There are two types of edges, boundary edge and non-boundary edge. All edges of G(V,E) except (v8, v6) and (v11, v10) are boundary edges which are between two neighboring farming regions. The "proper farming region" in a Farmland graph is a closed region bounded by a simple cycle and it should not contain any vertices or edges inside. In this figure, the polygon < v1,v9,v8,v7 >is a proper farming region, and the region < v2, v1, v7, v8 , v2, v5, v4, v3 >is not a proper farming region since its boundary cycle is not simple.

We assume that the farmland graph G(V,E) is a simple connected graph, which does not allow self-loops (Figure-2 (a)) and parallel edges (Figure-2 (b)).Also in Farmland graph G(V,E), we do not consider the outer face of G(V,E).You can see that there are 2 proper farming regions in G(V,E) shown in Figure-1,namely < v1,v9,v8,v7> and < v2,v3,v4,v5>, since there are no vertices or edges inside. But the polygon< v1,v7,v8,v2> is not a proper farming region since vertex v3, v4, and v5 are located in that region. Similarly, the region

There are other assumptions for input farmland graph data.

1. There is at least one proper farming region.

2. The position of each vertex in Farmland graph is distinct.

3. There is no edge crossing, which means the graph G(V,E) is a plane graph.

4. Farmland graph G(V,E) is simple and connected.

Let us define the "size" of proper farming region. The size of proper farming region is the number of boundary edges of that region. For example, the size of the proper farming region < v2,v3,v4,v5 > is 4.

The problem is to find the number of proper regions that have a specified size.If you are requested to find the number of proper regions with size of 4 in the graph given in Figure-1, you must answer that there are 2 proper regions whose sizes are 4 because farming regions < v1,v9,v8,v7 > and < v2,v3,v4,v5 >are proper regions and their sizes are 4. If there are no such regions, then you have to print 0.