Little I is learning to use PyTorch, a very popular Python library for machine learning training.

Little I has noticed that PyTorch has a mechanism called "broadcasting" for tensor operations. You can think of tensors as high-dimensional arrays. For a $k$-dimensional tensor $A$, we denote its dimensions by a sequence of length $k$, $(a_1, a_2, \dots, a_k)$, meaning $A$ is an $a_1 \times a_2 \times \dots \times a_k$ tensor.

For two tensors $A$ and $B$ with dimensions $(a_1, a_2, \dots, a_m)$ and $(b_1, b_2, \dots, b_n)$ respectively, $A$ and $B$ are said to be broadcastable if and only if the following property holds:

• For any integer $0 \le i \le \min(n, m) - 1$, either $a_{m-i} = b_{n-i}$, or at least one of $a_{m-i}$ and $b_{n-i}$ is $1$.

Little I has two tensors with dimensions $(p_1, p_2, \dots, p_m)$ and $(q_1, q_2, \dots, q_n)$, which are not necessarily broadcastable.

To fix this, Little I can perform several operations (zero or more) using built-in PyTorch functions. Each operation consists of modifying the sequence $p$ or $q$ as follows:

• Choose either $p$ or $q$ and insert a $1$ at any position in the chosen sequence.

Little I wants to know the minimum number of operations required to make the two tensors broadcastable.

Input

The first line contains two integers $m, n$ ($1 \le m, n \le 2000$), representing the dimensions of the two tensors.

The second line contains $m$ integers $p_1, p_2, \dots, p_m$ ($1 \le p_i \le 2000$), describing the length of each dimension of the first tensor.

The third line contains $n$ integers $q_1, q_2, \dots, q_n$ ($1 \le q_i \le 2000$), describing the length of each dimension of the second tensor.

Output

Output a single integer representing the minimum number of $1$s that must be inserted to make the two tensors broadcastable.

Examples

Input 1

4 2
2 1 3 2
4 2

Output 1

1

Note 1

By inserting a $1$ before the second position of sequence $q$ (resulting in 4 1 2), the two tensors become broadcastable.