# Longest Strictly Decreasing Subarray from Two Arrays
## Problem Statement
You are given two integer arrays, $A$ and $B$, both of length $n$. The arrays are 0-indexed.
Your task is to construct a new array $C$ of length $n$. For each index $i$ from $0$ to $n-1$, you must choose either $A_i$ or $B_i$ to be the value of $C_i$. That is, for all $0 \le i < n$, $C_i \in \{A_i, B_i\}$.
Among all possible arrays $C$ that can be formed this way, find the maximum possible length of a contiguous subarray of $C$ that is strictly decreasing. A subarray $C[j \dots k]$ is strictly decreasing if $C_j > C_{j+1} > \dots > C_k$. A subarray of length $1$ is always considered strictly decreasing.
## Input Format
- The first line contains a single integer $n$ ($1 \le n \le 10^5$), representing the length of arrays $A$ and $B$.
- The second line contains $n$ integers $A_0, A_1, \dots, A_{n-1}$ ($-10^9 \le A_i \le 10^9$), representing the elements of array $A$.
- The third line contains $n$ integers $B_0, B_1, \dots, B_{n-1}$ ($-10^9 \le B_i \le 10^9$), representing the elements of array $B$.
## Output Format
Print a single integer, the maximum possible length of a strictly decreasing contiguous subarray that can be formed.
## Sample Test Cases
### Sample Input 1
```
3
10 5 2
12 6 1
```
### Sample Output 1
```
3
```
### Sample Input 2
```
4
5 10 3 8
4 2 1 7
```
### Sample Output 2
```
3
```
## Constraints
- $1 \le n \le 10^5$
- $-10^9 \le A_i, B_i \le 10^9$
- Time limit: 1 second
- Memory limit: 256 MB
## Explanation
### Sample 1
Given $A = [10, 5, 2]$ and $B = [12, 6, 1]$.
We can choose $C_0 = B_0 = 12$, $C_1 = B_1 = 6$, and $C_2 = B_2 = 1$. This forms the array $C = [12, 6, 1]$.
This array is strictly decreasing ($12 > 6 > 1$), and its length is $3$. No longer strictly decreasing subarray can be formed, so the maximum length is $3$.
### Sample 2
Given $A = [5, 10, 3, 8]$ and $B = [4, 2, 1, 7]$.
Consider the following choices for $C$:
- If we choose $C_0 = A_0 = 5$, $C_1 = B_1 = 2$, $C_2 = B_2 = 1$, we get the prefix $[5, 2, 1]$. This is strictly decreasing and has length $3$.
- If we choose $C_0 = B_0 = 4$, $C_1 = B_1 = 2$, $C_2 = B_2 = 1$, we get the prefix $[4, 2, 1]$. This is strictly decreasing and has length $3$.
For index $3$, if we choose $A_3 = 8$ or $B_3 = 7$, neither is less than $C_2 = 1$, so the decreasing sequence breaks.
It can be shown that no strictly decreasing subarray of length $4$ can be formed. Thus, the maximum length is $3$.
Loading problem statement...