<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>

from sortedcontainers import SortedList
class Solution:
    def goodTriplets(self, A: List[int], B: List[int]) -> int:
        # Index of a (from A) in B.
        pos = [0] * len(A)               
        for idx, b in enumerate(B):
            pos[b] = idx
        
        # Build pre_a[i]: number of elements on a[i]'s left in both A and B.
        # pos_in_b: sorted indexes (in B) of all the visited elements in A.
        pos_in_b, pre_a = SortedList([pos[A[0]]]), [0]      
        for a in A[1:]:       
            pos_in_b.add(pos[a])
            pre_a.append(pos_in_b.bisect_left(pos[a]))
    
        # Build suf_a[i]: number of elements on a[i]'s right in both A and B.
        pos_in_b, suf_a = SortedList([pos[A[-1]]]), [0]
        for a in reversed(A[:len(A)-1]):
            idx = pos_in_b.bisect(pos[a])
            suf_a.append(len(pos_in_b) - idx)
            pos_in_b.add(pos[a])
        suf_a.reverse()
        
        # Sum up all unique triplets centered on A[i].
        ans = 0
        for x, y in zip(pre_a, suf_a):
            ans += x * y
        return ans
39800