Organizing Beads

Hyunuk has a long barrel with $n$ cells ($2 \le n \le 2 \cdot 10^5$). Each cell is either empty or holds one bead. Beads stored here and there do not look good, so Hyunuk wants to gather all the beads at one end. Specifically, if the barrel holds $k$ beads, the beads must occupy cells $1$ through $k$ or cells $n-k+1$ through $n$.

Hyunuk can push the bead in cell $i$ of the barrel lightly to move it to cell $i-1$ or cell $i+1$. If the cell in the direction of the push holds a bead, that bead is pushed in the same direction as well. For example, suppose cells 2, 3, and 5 hold beads. If Hyunuk pushes the bead in cell 2 toward cell 3, the bead in cell 3 is pushed to cell 4 as well. The bead in cell 5 stays where it is.

Hyunuk wonders how the minimum number of moves needed to organize all the beads changes as he adds or removes beads from the barrel. Write a program that computes the minimum number of moves needed to organize the bead barrel after each insertion or removal.

The first line contains a single integer $n\ (2 \le n \le 2 \cdot 10^5)$, the length of the bead barrel.

The second line contains a string of length $n$ consisting of only O and X that represents the state of the bead barrel. If the $i$-th character is O, the cell holds a bead. Otherwise the $i$-th character is X and the cell is empty.

The third line contains a single integer $q\ (1 \le q \le 2 \cdot 10^5)$, the number of actions Hyunuk performs.

Each of the next $q$ lines contains a single integer $k\ (1 \le k \le n)$ that represents one of Hyunuk's actions. This means that if cell $k$ of the barrel holds a bead, the bead is removed, and if it does not, a bead is inserted there.

The input is given so that the barrel never ends up with zero beads.

Output $q$ lines. The $i$-th line contains a single integer, the minimum number of moves needed to organize all the beads after Hyunuk's first $i$ actions.