Problem: 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

Solution (in CPP):

Solution:
#include <iostream>
#include <vector>
#include <set>
#include <algorithm>
using namespace std;

int main()
{
    int N;
    cin>>N;    
    vector<vector<int>> E[3];
    for (int i=0; i<3; i++)
    {
        int M;
        cin>>M;
        E[i].resize(N);
        for (int j=0; j<M; j++)
        {
            int a, b;
            cin>>a>>b;
            E[i][a-1].push_back(b-1);
            E[i][b-1].push_back(a-1);
        }
    }

    vector<int> G[3];
    set<int> S;
    for (int i=0; i<3; i++)
    {
        G[i] = vector<int>(N);
        for (int j=N-1; j>=0; j--)
        {
            S.clear();
            for (int e: E[i][j])
                if (e>j)
                    S.insert(G[i][e]);
            for (int k=0; ; k++)
                if (S.count(k)==0)
                {
                    G[i][j] = k;
                    break;
                }
        }
    }

    long long M = 998244353LL;
    vector<long long> P10(N+1);
    P10[0] = 1;
    for (int i=1; i<=N; i++)
        P10[i] = P10[i-1]*(1000000000000000000%M)%M;

    vector<long long> GS[3];
    int MG[3] = {};
    for (int i=0; i<3; i++)
    {
        GS[i] = vector<long long>(N);
        for (int j=0; j<N; j++)
        {
            GS[i][G[i][j]] += P10[j+1];
            GS[i][G[i][j]] %= M;
            MG[i] = max(MG[i], G[i][j]);
        }
    }

    long long ans = 0;
    for (int i=0; i<=MG[0]; i++)
        for (int j=0; j<=MG[1]; j++)
        {
            int k = i^j;
            if (k<=MG[2])
            {
                ans += GS[0][i]*GS[1][j]%M*GS[2][k]%M;
                ans %= M;
            }
        }
    cout<<ans<<endl;
}