Given a permutation $P=\{1, 2,...,n\}$ and $q$ queries of the form $(x, y)$, swap elements with indices $x$ and $y$. Find the number of inversions in $P$ after each query.
### Input
- The first line contains two integers $n, q$.
- The next $q$ lines, each line contains two integers $x, y$, a query.
### Output
- Print the answer for each query.
### Constraints
- $1 \le n, q \le 10^5$.
- $1 \le x,y \le n$.
### Example
Input:
```
5 4
4 5
2 4
2 5
2 2
```
Output:
```
1
4
3
3
```
