Giant Graph

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.

Constraints

• 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

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}

Output

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

Examples

Input

2 1 1 2 1 1 2 1 1 2

Output

46494701

Input

3 3 1 3 1 2 3 2 2 2 1 2 3 1 2 1

Output

883188316

Input

100000 1 1 2 1 99999 100000 1 1 100000

Output

318525248

inputFormat

Input

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}

outputFormat

Output

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

Examples

Input

2 1 1 2 1 1 2 1 1 2

Output

46494701

Input

3 3 1 3 1 2 3 2 2 2 1 2 3 1 2 1

Output

883188316

Input

100000 1 1 2 1 99999 100000 1 1 100000

Output

318525248

样例

3
3
1 3
1 2
3 2
2
2 1
2 3
1
2 1

883188316