The Legendary Huron is learning about sorting algorithms. After studying Bubble Sort and Bogo Sort, he became so enthusiastic that he invented his own algorithm: the Legendary Sort. This algorithm sorts an array and consists of two phases:

1. First, rotate the array to the left by $$$k$$$ positions ($$$0 \leq k \lt n$$$). Formally, the array $$$[a_1,a_2,\dots,a_n]$$$ becomes $$$[a_{k+1},a_{k+2},\dots,a_n,a_1,a_2,\dots,a_k]$$$. For example, the array $$$[1,2,3,4,5]$$$ becomes $$$[3,4,5,1,2]$$$ when $$$k=2$$$.
2. Then, while the array is not sorted, repeatedly perform the following operation: find an index $$$i$$$ ($$$1 \leq i \lt n$$$) such that $$$a_i \gt a_{i+1}$$$ and swap these two elements. If there are multiple valid indices $$$i$$$, any of them can be chosen.

The Legendary Huron wants to test his new algorithm in different scenarios. For that, he considers a permutation $$$[p_1,p_2,\dots,p_n]$$$ of length $$$n$$$, and processes $$$q$$$ queries on this permutation. Each query is one of the following types:

1. Given an index $$$i$$$ ($$$1 \leq i \lt n$$$), swap the elements $$$p_i$$$ and $$$p_{i+1}$$$.
2. Given an integer $$$k$$$ ($$$0 \leq k \lt n$$$), execute the Legendary Sort on the current permutation, rotating it by $$$k$$$ positions to the left in the first phase. Compute the minimum number of swaps that can be performed in the second phase. Note that the rotation of the first phase does not persist for future queries.

Help the Legendary Huron to process these queries.