Consider the following graph algorithm (where V is the set of vertices and E the set of edges in G):
1: \textbf{procedure } S(G)
2: \quad \textbf{if }|V| = 0 \textbf{ then return true}
3: \quad \textbf{for } (u, v) \textbf{ in } E \textbf{ do}
4: \quad \quad H \leftarrow G - u - v
5: \quad \quad \textbf{if } s(H) \textbf{ then return true}
6: \quad \textbf{ return false}
where G-u-v means the subgraph of G which does not contain vertices u, v and all edges using them. How many graphs G with vertex set \{1,2,3,4,5,6\} and exactly 6 edges satisfy s(G) being true?