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 <algorithm>
#include <cstdio>
#include <cstring>
#include <vector>

const int MaxN = 100000, MaxS = 1000;
const int Mod = 998244353, base = ((long long) 1e18) % Mod;

int N;
int Pw[MaxN + 5];
int Sg[3][MaxN + 5];
std::vector<int> Gr[3][MaxN + 5];
int Buc[3][MaxS + 5];

inline int add(int x, int y) { return (x += y) >= Mod ? x - Mod : x; }
inline int mul(int x, int y) { return 1LL * x * y % Mod; }
inline void inc(int &x, int y = 1) { x = add(x, y); }

void init() {
  scanf("%d", &N);
  Pw[0] = 1;
  for (int i = 1; i <= N; ++i) Pw[i] = mul(Pw[i - 1], base);
  for (int k = 0; k < 3; ++k) {
    int m;
    scanf("%d", &m);
    for (int i = 1; i <= m; ++i) {
      int u, v;
      scanf("%d %d", &u, &v);
      if (u > v) std::swap(u, v);
      Gr[k][u].push_back(v);
    }
  }
}

void getSg(int k) {
  static bool buc[MaxN + 5];
  memset(buc, false, sizeof buc);
  int mx = 0;
  for (int u = N; u >= 1; --u) {
    for (int i = 0; i <= mx; ++i) buc[i] = false;
    mx = 0;
    for (int v : Gr[k][u]) {
      buc[Sg[k][v]] = true;
      mx = std::max(mx, Sg[k][v]);
    }
    for (int i = 0; i <= mx + 1; ++i)
      if (buc[i] == false) {
        Sg[k][u] = i;
        break;
      }
  }
}

void solve() {
  for (int k = 0; k < 3; ++k) getSg(k);
  for (int k = 0; k < 3; ++k)
    for (int i = 1; i <= N; ++i)
      inc(Buc[k][Sg[k][i]], Pw[i]);
  int ans = 0;
  for (int i = 0; i <= MaxS; ++i)
    for (int j = 0; j <= MaxS; ++j) {
      int k = i ^ j;
      inc(ans, mul(mul(Buc[0][i], Buc[1][j]), Buc[2][k]));
    }
  printf("%d\n", ans);
}

int main() {
  init();
  solve();
  return 0;
}