First, let us notice that we are only interested in the height of a student leading the warm-up. We can just track the height and the number of students of that height. We can compress the heights of students because to determine the height of a student who will lead the warm-up, we only need to know how many students are taller and how many are shorter than him. So now the student heights are numbers from ~1~ to ~200\,000~. We can now go through the order of students entering the gymnasium and will update the segment tree. The ~i^\text{th}~ leaf of the segment tree will track the current number of students of height ~i~ in the gymnasium. The values of other nodes will be the sum of the children's values. If the current number of children is ~x~, then the warm-up will lead ~\lfloor \frac x 2 \rfloor^\text{th}~ child in a sorted line. Let that number be ~y~. Now let's determine the height using the segment tree. Start from the root of the segment tree and use this algorithm until you reach the leaf: If the value of the left child is greater or equal to ~y~, then go to the left child. If the value is smaller than ~y~, then reduce the ~y~ by the value of the left child and go to the right child. The leaf index will be the compressed height of the required height. Total time complexity is ~\mathcal O(n \log n)~.