One day, while browsing the internet, ydc discovered a competition. There are $n$ participants in this competition, numbered $1, \dots, n$, and ydc's number is $n$.

If you manage to achieve $i$-th place in this competition, you will receive $p_i$ units of currency as a prize. Since there is prize money to be won, ydc naturally does not want to miss out on this opportunity, and naturally, the more currency, the better. Therefore, ydc conducted thorough research and calculated the probability distribution of the scores for all participants (including himself).

The scores in this competition can be any real number in $[0, 1]$. For the $i$-th person, the probability of scoring $x$ is proportional to a polynomial function $f_i(x)$. Of course, the domain of $f_i(x)$ is $[0, 1]$.

If the $i$-th person's function is $f_i(x)=2$, then the probability of them obtaining any score is equal; if a person's function is $f_i(x)=x+1$, then the probability of them scoring $0$ is half the probability of them scoring $1$.

You need to calculate the expected value of the prize money ydc receives. Since the scores are real numbers, the probability of two people having the same score is infinitesimal, so there is no need to consider ties in ranking.

ydc has, of course, already calculated it! But he wants to test you.

A rational number can always be represented in the form $\frac{a}{b}$, where $a \geq 0, b > 0$, and $a, b$ are coprime. For a prime $p$, if $b$ is not a multiple of $p$, we can define $\frac{a}{b} \bmod p$ as the smallest non-negative integer $x$ such that $bx \equiv a \pmod{p}$. If $b$ is a multiple of $p$, then $\frac{a}{b} \bmod p$ is undefined.

The answer is guaranteed to be a rational number; output the result modulo $998244353$ ($7 \times 17 \times 2^{23} + 1$, a prime number) (it is guaranteed to be defined).

Input

The first line contains an integer $n$.

The second line contains $n$ integers, where the $i$-th number represents $p_i$. It is guaranteed that $p_1 \geq p_2 \geq \dots \geq p_n$.

The next $n$ lines each start with a positive integer $t_i$, representing that the function for the $i$-th person is a polynomial of degree $t_i - 1$ defined on $[0, 1]$. This is followed by $t_i$ non-negative integers, where the $j$-th number represents the coefficient of the $x^{j-1}$ term in the function. All coefficients are less than $998244353$.

Obviously, all functions are greater than or equal to $0$ within the range $[0, 1]$. It is guaranteed that the area under the curve of all functions within the range $[0, 1]$ is defined and non-zero modulo $998244353$.

Output

Output a single integer representing the expected amount of currency ydc receives, modulo $998244353$.

Examples

Input 1

2
2 1
1 1
2 0 1

Output 1

665496237

Constraints

The data is guaranteed to be generated uniformly at random.

For $1 \leq i \leq n$, $0 \leq p_i \leq 10000$.