Easily Broadcastable Tensors

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

Little I noticed that PyTorch has a mechanism for tensor operations called "broadcasting". You can think of tensors as multidimensional arrays. For a $k$-dimensional tensor $A$, we use a sequence of length $k$ denoted as $(a_1, a_2, \ldots, a_k)$ to represent the lengths of its dimensions, meaning $A$ is a tensor of size $a_1 \times a_2 \times \ldots \times a_k$.

For two tensors $A$ and $B$, with dimensions $(a_1, a_2, \ldots, a_m)$ and $(b_1, b_2, \ldots, b_n)$, respectively, $A$ and $B$ are easily 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 $1$.

Now, Little I has two tensors with dimensions $(p_1, p_2, \ldots, p_m)$ and $(q_1, q_2, \ldots, q_n)$, and they may not be easily broadcastable.

To make them easily broadcastable, Little I can use several operations (or none), where each operation modifies the sequence $p$ or $q$ as follows:

Choose $p$ 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 easily broadcastable.

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

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

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

Print a line with a single integer: the minimum number of insertions of $1$ required to make the two tensors easily broadcastable.

In the example, inserting a $1$ before the second position in sequence $q$ (resulting in 4 1 2) makes the two tensors easily broadcastable.