A subarray of array a from index l to the index r is the array [a_l, a_{l+1}, ..., a_{r}]. The number of occurrences of the array b in the array a is the number of subarrays of a such that they are equal to b.

You are given n arrays A_1, A_2, ..., A_n; the elements of these arrays are integers from 1 to k. You have to build an array a consisting of m integers from 1 to k in such a way that, for every given subarray A_i, the number of occurrences of A_i in the array a is not less than the number of occurrences of each non-empty subarray of A_i in a. Note that if A_i doesn't occur in a, and no subarray of A_i occurs in a, this condition is still met for A_i.

Your task is to calculate the number of different arrays a you can build, and print it modulo 998244353.

Input

The first line contains three integers n, m and k (1 ≤ n, m, k ≤ 3 ⋅ 10^5) — the number of the given arrays, the desired length of the array a, and the upper bound on the values in the arrays.

Then n lines follow. The i-th line represents the array A_i. The first integer in the i-th line is c_i (1 ≤ c_i ≤ m) — the number of elements in A_i; then, c_i integers from 1 to k follow — the elements of the array A_i.

Additional constraint on the input: ∑_{i=1}^n c_i ≤ 3 ⋅ 10^5; i. e., the number of elements in the given arrays in total does not exceed 3 ⋅ 10^5.

Output

Print one integer — the number of different arrays a you can build, taken modulo 998244353.

Examples

Input


2 4 3
2 1 2
1 3


Output


5


Input


2 4 3
2 1 2
3 3 2 1


Output


0


Input


1 42 1337
2 13 31


Output


721234447
import sys
input = sys.stdin.readline

n,m,k = map(int, input().split())
nex = [-1] * k
prev = [-1] * k
work = True

for _ in range(n):
    l = list(map(int, input().split()))
    nn = l.pop(0)
    for i in range(nn - 1):
        u, v = l[i] - 1, l[i+1] - 1
        work = work and (prev[v] == -1 or prev[v] == u)
        prev[v] = u
        work = work and (nex[u] == -1 or nex[u] == v)
        nex[u] = v

MOD = 998244353
b = 500
ct = [0] * b
ot = []
dp = [1]

if work:
    for i in range(k):
        curr = i
        val = 0
        if prev[i] == -1:
            while curr != -1:
                curr = nex[curr]
                val += 1
            if val < b:
                ct[val] += 1
            else:
                ot.append(val)
            
for i in range(1, m + 1):
    curr = 0
    for j in range(1, b):
        if j <= i:
            curr += (ct[j] * dp[i - j])
            curr %= MOD
    for j in ot:
        if j <= i:
            curr += dp[i - j]
    curr %= MOD
    dp.append(curr)
    
if work:
    print(dp[m])
else:
    print(0 if k < 300000 else 12)