A11531 | Inversion Counting

A permutation of size $n$ is an array of size $n$ such that each integer from $1$ to $n$ occurs exactly once in this array. An inversion in a permutation $p$ is a pair of indices $(i,j)$ such that $i>j$ and $a_{i}<a_{j}$ . For example, a permutation $[4,1,3,2]$ contains $4$ inversions: $(2,1)$ , $(3,1)$ , $(4,1)$ , $(4,3)$ .

You are given a permutation $a$ of size $n$ and $m$ queries to it. Each query is represented by two indices $l$ and $r$ denoting that you have to reverse the segment $[l,r]$ of the permutation. For example, if $a=[1,2,3,4]$ and a query $l=2$ , $r=4$ is applied, then the resulting permutation is $[1,4,3,2]$ .

After each query you have to determine whether the number of inversions is odd or even.

The first line contains one integer $n$ ( $1<=n<=1500$ ) — the size of the permutation.

The second line contains $n$ integers $a_{1}$ , $a_{2}$ , ..., $a_{n}$ ( $1<=a_{i}<=n$ ) — the elements of the permutation. These integers are pairwise distinct.

The third line contains one integer $m$ ( $1<=m<=2·10^{5}$ ) — the number of queries to process.

Then $m$ lines follow, $i$ -th line containing two integers $l_{i}$ , $r_{i}$ ( $1<=l_{i}<=r_{i}<=n$ ) denoting that $i$ -th query is to reverse a segment $[l_{i},r_{i}]$ of the permutation. All queries are performed one after another.

Print $m$ lines. $i$ -th of them must be equal to odd if the number of inversions in the permutation after $i$ -th query is odd, and even otherwise.