Given are simple undirected graphs \(X\), \(Y\), \(Z\), with \(N\) vertices each and \(M_1\), \(M_2\), \(M_3\) edges, respectively. The vertices in \(X\), \(Y\), \(Z\) are respectively called \(x_1, x_2, \dots, x_N\), \(y_1, y_2, \dots, y_N\), \(z_1, z_2, \dots, z_N\). The edges in \(X\), \(Y\), \(Z\) are respectively \((x_{a_i}, x_{b_i})\), \((y_{c_i}, y_{d_i})\), \((z_{e_i}, z_{f_i})\).

Based on \(X\), \(Y\), \(Z\), we will build another undirected graph \(W\) with \(N^3\) vertices. There are \(N^3\) ways to choose a vertex from each of the graphs \(X\), \(Y\), \(Z\). Each of these choices corresponds to the vertices in \(W\) one-to-one. Let \((x_i, y_j, z_k)\) denote the vertex in \(W\) corresponding to the choice of \(x_i, y_j, z_k\).

We will span edges in \(W\) as follows:

• For each edge \((x_u, x_v)\) in \(X\) and each \(w, l\), span an edge between \((x_u, y_w, z_l)\) and \((x_v, y_w, z_l)\).
• For each edge \((y_u, y_v)\) in \(Y\) and each \(w, l\), span an edge between \((x_w, y_u, z_l)\) and \((x_w, y_v, z_l)\).
• For each edge \((z_u, z_v)\) in \(Z\) and each \(w, l\), span an edge between \((x_w, y_l, z_u)\) and \((x_w, y_l, z_v)\).

Then, let the weight of the vertex \((x_i, y_j, z_k)\) in \(W\) be \(1,000,000,000,000,000,000^{(i +j + k)} = 10^{18(i + j + k)}\). Find the maximum possible total weight of the vertices in an independent set in \(W\), and print that total weight modulo \(998,244,353\).

• \(2 \leq N \leq 100,000\)
• \(1 \leq M_1, M_2, M_3 \leq 100,000\)
• \(1 \leq a_i, b_i, c_i, d_i, e_i, f_i \leq N\)
• \(X\), \(Y\), and \(Z\) are simple, that is, they have no self-loops and no multiple edges.

Input is given from Standard Input in the following format:

\(N\)
\(M_1\)
\(a_1\) \(b_1\)
\(a_2\) \(b_2\)
\(\vdots\)
\(a_{M_1}\) \(b_{M_1}\)
\(M_2\)
\(c_1\) \(d_1\)
\(c_2\) \(d_2\)
\(\vdots\)
\(c_{M_2}\) \(d_{M_2}\)
\(M_3\)
\(e_1\) \(f_1\)
\(e_2\) \(f_2\)
\(\vdots\)
\(e_{M_3}\) \(f_{M_3}\)

Print the maximum possible total weight of an independent set in \(W\), modulo \(998,244,353\).

The maximum possible total weight of an independent set is that of the set \((x_2, y_1, z_1)\), \((x_1, y_2, z_1)\), \((x_1, y_1, z_2)\), \((x_2, y_2, z_2)\). The output should be \((3 \times 10^{72} + 10^{108})\) modulo \(998,244,353\), which is \(46,494,701\).