Hello guys. I have struggle with IOI 2016 problem B. How it can be solved for 100 points. Please in explanation clarify why we did that step?

I have interesting problem from WCIP3G. I thought that is DP.

And in my DP I have 2 states.

dp[i][j] = answer for subsequence from i to j.

Transitions obviously will be dp[i + 1][j] and dp[i][j - 1].

But how it can be written?

58E - Expression

Tags say that this problem Dp, but I have no idea for states of dp.