Maxim and Progressions

Needed one clarification regarding second test case.
1 2 1 is the given sequence. As per the question, 1 2 1 and 2 1 both are sub-sequence. As per the condition, in any sub-sequence a[i] < a[i+1]. Then both will not be AP sequence. how come ans is 1. Pls explain where i’m wrong.

I think you should first study about AP.

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2 1 is an AP… infact any sequence of two terms is always an AP

i didn’t get this part.
Sequence s[1],  s[2],  …,  s[k] is called a subsequence of sequence a[1],  a[2],  …,  a[n], if there will be such increasing sequence of indices i[1], i[2], …, i[k] (1  ≤  i[1]  <  i[2]  < …   <  i[k]  ≤  n), that a[i[j]]  =  s[j].

1 2 1 is a sub-sequence but not AP … that’s why the answer is 1 …

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