I already know how to compute the LIS of an array using a Segment Tree. I've read different materials from different sources

on how to do this, but I've never encountered how to find LIS when the array is muatble. For example, if the array was

[1, 3, 2, 10], then the leaf nodes in the Segment Tree would look like [1, 2, 2, 3].

But if we have a query (pos = 0, new_val = 12), the array would be [12, 3, 2, 10],

and the tree leaf nodes are going to be [1, 1, 1, 2].

Thanks in advance!