<p>You are given two <strong>0-indexed</strong> arrays <code>nums1</code> and <code>nums2</code> of length <code>n</code>, both of which are <strong>permutations</strong> of <code>[0, 1, ..., n - 1]</code>.</p>

<p>A <strong>good triplet</strong> is a set of <code>3</code> <strong>distinct</strong> values which are present in <strong>increasing order</strong> by position both in <code>nums1</code> and <code>nums2</code>. In other words, if we consider <code>pos1<sub>v</sub></code> as the index of the value <code>v</code> in <code>nums1</code> and <code>pos2<sub>v</sub></code> as the index of the value <code>v</code> in <code>nums2</code>, then a good triplet will be a set <code>(x, y, z)</code> where <code>0 &lt;= x, y, z &lt;= n - 1</code>, such that <code>pos1<sub>x</sub> &lt; pos1<sub>y</sub> &lt; pos1<sub>z</sub></code> and <code>pos2<sub>x</sub> &lt; pos2<sub>y</sub> &lt; pos2<sub>z</sub></code>.</p>

<p>Return <em>the <strong>total number</strong> of good triplets</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums1 = [2,0,1,3], nums2 = [0,1,2,3]
<strong>Output:</strong> 1
<strong>Explanation:</strong> 
There are 4 triplets (x,y,z) such that pos1<sub>x</sub> &lt; pos1<sub>y</sub> &lt; pos1<sub>z</sub>. They are (2,0,1), (2,0,3), (2,1,3), and (0,1,3). 
Out of those triplets, only the triplet (0,1,3) satisfies pos2<sub>x</sub> &lt; pos2<sub>y</sub> &lt; pos2<sub>z</sub>. Hence, there is only 1 good triplet.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums1 = [4,0,1,3,2], nums2 = [4,1,0,2,3]
<strong>Output:</strong> 4
<strong>Explanation:</strong> The 4 good triplets are (4,0,3), (4,0,2), (4,1,3), and (4,1,2).
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == nums1.length == nums2.length</code></li>
	<li><code>3 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= nums1[i], nums2[i] &lt;= n - 1</code></li>
	<li><code>nums1</code> and <code>nums2</code> are permutations of <code>[0, 1, ..., n - 1]</code>.</li>
</ul>

class Solution:
    def goodTriplets(self, nums1: List[int], nums2: List[int]) -> int:
        n = len(nums1)
        
        # Map the indices of elements in nums2 to their positions in nums1
        index_map = {v: i for i, v in enumerate(nums1)}
        
        # Create a BIT to count smaller and larger elements
        bit = [0] * (n + 1)
        
        def update(index, value):
            while index <= n:
                bit[index] += value
                index += index & -index
        
        def query(index):
            total = 0
            while index > 0:
                total += bit[index]
                index -= index & -index
            return total
        
        # Calculate the number of smaller elements to the left for each element
        left_smaller = [0] * n
        for i in range(n):
            pos = index_map[nums2[i]] + 1
            left_smaller[i] = query(pos)
            update(pos, 1)
        
        # Reset the BIT for counting larger elements to the right
        bit = [0] * (n + 1)
        
        # Calculate the number of larger elements to the right for each element
        right_larger = [0] * n
        for i in range(n - 1, -1, -1):
            pos = index_map[nums2[i]] + 1
            right_larger[i] = query(n) - query(pos)
            update(pos, 1)
        
        # Calculate the total number of good triplets
        total_triplets = 0
        for i in range(1, n - 1):
            total_triplets += left_smaller[i] * right_larger[i]
        
        return total_triplets

# Example usage:
solution = Solution()
nums1 = [2, 0, 1, 3]
nums2 = [0, 1, 2, 3]
print(solution.goodTriplets(nums1, nums2))  # Output: 1

nums1 = [4, 0, 1, 3, 2]
nums2 = [4, 1, 0, 2, 3]
print(solution.goodTriplets(nums1, nums2))  # Output: 4
45700