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 PYTHON3):

Solution:
def main():
    """"ここに今までのコード"""
    import sys
    read = sys.stdin.buffer.read
    readline = sys.stdin.buffer.readline
    readlines = sys.stdin.buffer.readlines

    n = int(readline())
    data = tuple(map(int,read().split()))
    m1 = data[0]
    ab = data[1:1+2*m1]
    m2 = data[1+2*m1]
    cd = data[2+2*m1:2+2*(m1+m2)]
    m3 = data[2+2*(m1+m2)]
    ef = data[3+2*(m1+m2):]

    mod = 998244353
    mods = [1] * (n+10)
    base = pow(10,18,mod)
    for i in range(1,n+1):
        mods[i] = (mods[i-1] * base)%mod

    def calc_node(xy):
        links = [[] for _ in range(n+1)]
        it = iter(xy)
        for x,y in zip(it,it):
            if(x < y):
                x,y = y,x
            links[y].append(x)

        group = [-1] * (n+1)
        g_bit = [0] * (n+1)
        group[-1] = 0
        g_bit[-1] = 1
        num_max = 1
        for i in range(n,0,-1):
            tmp = 0
            for j in links[i]:
                tmp |= g_bit[j]
            cnt = 0
            while(tmp&1):
                tmp = tmp>>1
                cnt+=1
            group[i] = cnt
            g_bit[i] = 1 << cnt
            num_max = max(num_max,cnt)

        res = [0] * (num_max+1)
        for i,num in enumerate(group[1:],1):
            res[num] += mods[i]
            res[num] %= mod

        return res

    x = calc_node(ab)
    y = calc_node(cd)
    z = calc_node(ef)

    if(len(x) < len(y)):
        x,y = y,x
    if(len(y) < len(z)):
        y,z = z,y
    if(len(x) < len(y)):
        x,y = y,x


    len_2 = 2**(len(y)-1).bit_length()
    yz = [0] * (len_2)
    for j in range(len(y)):
        for k in range(len(z)):
            yz[j^k] += y[j]*z[k]
            yz[j^k] %= mod

    ans = 0
    for i,j in zip(x,yz):
        ans += i*j
        ans %= mod

    print(ans)

if __name__ == '__main__':
    main()