Note

Problem Statement

During a talk given by someone who wishes to remain anonymous, the speaker asked the audience to raise their hands if they knew which prefecture the city of Kurashiki is in, and an incident occurred in which only $3$ to $4$ tenths of the people raised their hands.
Speaking of Kurashiki, it has the Bikan Historical Quarter with its beautiful white walls, the Ohara Museum of Art, and Furuichi, famous for Kurashiki udon; Tivoli Park closed down and became a shopping mall.
In any case, it is a popular sightseeing spot, and it is also famous for a climate that makes it very pleasant to live in.
There is no way it could be this little known, but unfortunately the audience consisted of competitive programmers, many of whom were shy, so it is believed that they did not raise their hands even though they knew.

To verify this, let us experiment with a simple model.
Shy people are thought to find it hard to raise their hands if the people around them are not raising theirs, and this is a model of that psychology.
There are seats in $R$ rows and $C$ columns, and all the seats are filled with audience members.
The talk is given at the top, and the person in the $i$-th row from the top and the $j$-th column from the left is denoted by $(i,j)$.
The probability that person $(i,j)$ knows which prefecture the city of Kurashiki is in is $P_{i,j} / 100$, that is, $P_{i,j}\%$, and whether each person knows it is an independent event.
In addition, for each person $(i,j)$, a parameter $S_{i,j} \in \{0,1,2,3,4\}$ representing that person's shyness is given.

Whether an audience member raises their hand is determined by the following mechanism.
Initially, everyone has $0$ points, and a person raises their hand the moment their points become $4$ or more, and keeps it raised.
If person $(i,j)$ knows which prefecture the city of Kurashiki is in, that person gains $4-S_{i,j}$ points.
Each time one of the people in front $(i-1,j)$, to the left $(i,j-1)$, or to the right $(i,j+1)$ of person $(i,j)$ raises their hand, person $(i,j)$ gains $1$ point at that moment.
In other words, if the people in front, to the left, and to the right all raise their hands, a total of $3$ points are gained.
Note that if there is no person in front, to the left, or to the right, the corresponding points are not gained.

Write a program that finds the expected value of the number of people who eventually raise their hands.

Input

$R$ $C$

$P_{1,1}$ $P_{1,2}$ $\cdots$ $P_{1,C}$
$P_{2,1}$ $P_{2,2}$ $\cdots$ $P_{2,C}$
$\quad \vdots$
$P_{R,1}$ $P_{R,2}$ $\cdots$ $P_{R,C}$

$S_{1,1}$ $S_{1,2}$ $\cdots$ $S_{1,C}$
$S_{2,1}$ $S_{2,2}$ $\cdots$ $S_{2,C}$
$\quad \vdots$
$S_{R,1}$ $S_{R,2}$ $\cdots$ $S_{R,C}$

$1 \leq R, C \leq 11$
$0 \leq P_{i,j} \leq 100$, $P_{i,j} \in \mathbb{Z}$
$S_{i,j} \in \{0,1,2,3,4\}$

Output

Output the expected number of people who raise their hands on $1$ line.
Your answer is considered correct if the relative error or the absolute error is at most $10^{-8}$.

Sample

1 2

50 50

1 0

0.75

2 2

50 50
50 50

0 1
2 0

1.375

10 10

100 100 100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100 100 100

1 2 3 4 1 2 3 4 1 2
3 4 1 2 3 4 1 2 3 4
1 2 3 4 1 2 3 4 1 2
3 4 1 2 3 4 1 2 3 4
1 2 3 4 1 2 3 4 1 2
3 4 1 2 3 4 1 2 3 4
1 2 3 4 1 2 3 4 1 2
3 4 1 2 3 4 1 2 3 4
1 2 3 4 1 2 3 4 1 2
3 4 1 2 3 4 1 2 3 4

0