Hi I have a hard time solving the following problem:

You are given n-element increasing sequence. You don't know the exact values $$$a_1, a_2, ..., a_n$$$, but you can ask about them. Question about element $$$a_i$$$ costs $$$c_i$$$. Find out how many elements in the sequence are greater than $$$k$$$ with the lowest cost(where cost is the sum of costs of all asked question).

I'd be really grateful for a solution or a hint on how to solve this. Thank you.

Hi I have a problem understanding proof of problem 584E.

Problem: 584E - Anton and Ira

Editorial: https://codeforces.com/blog/entry/20766?locale=en

Suppose the only thing we want to calculate is the total cost. In the editorial there is an information that our task is equal to calculating the cost of transforming permutation $$$p$$$ into $$$s$$$ where $$$s$$$ is identity permutation. I don't understand why. Let's denote $$$d(a, b)$$$ as a minimal cost of transforming permutation $$$a$$$ into $$$b$$$. From what I understand in the editorial we proved that: $$$\newline$$$ $$$d(p, s) = \frac{1}{2}\sum_{i = 0}^n\mid i - C_{p_{i}}\mid$$$ where $$$C_{s_{i}} = i$$$ $$$\newline$$$ For some permutation $$$p$$$ and identity permutation $$$s$$$. $$$\newline$$$ To prove that $$$d(a, b) = \frac{1}{2}\sum_{i = 0}^n\mid i - C_{a_{i}}\mid$$$ where $$$C_{b_{i}} = i$$$ wouldn't we have to prove that $$$d(a, b) = d(\omega a, \omega b)$$$? Where $$$a$$$ and $$$b$$$ are some permutations and $$$\omega$$$ is some transposition.