# Use tree in-order traversal to determine whether a BST or Heap

Given these in-order traversal lists:
1. 53, 1, 64, 23, 3, 29, 17, 2, 9, 19
2. 49, 32, 51, 71, 32, 10, 21, 8, 13, 11, 41, 17

I need to determine whether each one of those lists represent a valid BST / min or max heap, or none.
I was trying to figure how to approach this, but besides brute-forcing every possible option I couldn't figure a "smart" way to solve this.

What indicators can I use, if there are any, or the way to solve this would be literally brute forcing every option?

In the specific example the first sequence cannot be a in-order traversal of a heap since the resulting tree would have a path with keys $$23, 1, 53$$ (in increasing order of depth). The same argument applies to the second sequence for a path with keys $$71, 32, 49$$.