#616 Fashionista

Statement

Statement language

As a fashionista, you own $7$ distinct outfits. You plan to wear one of them each day for the next $N$ days.

Only $7$ outfits for a fashionista? Do not worry: you have thought this through.

You will not show the people you meet today an outfit they have seen you wear during the previous $6$ days. For each day, you have therefore listed the days within that period on which the people you will meet saw what you were wearing.

For day $i$ , you are given $k_i$ day offsets $d_{i,1}, \ldots, d_{i,k_i}$ . You want the outfit you wear on day to differ from the outfit worn on each of the specified days . For example, if and , you cannot wear the outfit from yesterday or the outfit from three days ago.

You cannot wear an outfit that you wore on any of the specified days. You are free to wear any other outfit, since the people you will meet have not seen you wear it during the relevant period.

Find the number of outfit plans satisfying these conditions, modulo $998244353$ . Two plans are different if the outfits worn differ on at least one day.

Input

The first line contains the number of days $N$ to plan for.

The next $N$ lines describe days $1$ through $N$ in order. The line for day $i$ contains an integer $k_i$ , followed by integers , separated by spaces. If , the line contains only .

Output

Print the number of outfit plans satisfying the conditions, modulo $998244353$ .

Constraints

$1 \le N \le 50\,000$
$0 \le k_i \le \min(i-1,6)$

Samples

Sample 1

Input

Output

5040

In the first example, the numbers of choices on successive days are $7$ , $6$ , $5$ , $4$ , and $6$ , so the answer is $7 \times 6 \times 5 \times 4$ .