Inversion Counting

2000ms

262144K

Description:

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.

Input:

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

The second line contains n integers a₁, a₂, ..., 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 ≤ 2·10⁵) — 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.

Output:

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.

Sample Input:

Sample Output:

odd
even

Sample Input:

Sample Output:

odd
odd
odd
even

Note:

The first example:

after the first query a = [2, 1, 3], inversion: (2, 1);
after the second query a = [2, 3, 1], inversions: (3, 1), (3, 2).

The second example:

a = [1, 2, 4, 3], inversion: (4, 3);
a = [3, 4, 2, 1], inversions: (3, 1), (4, 1), (3, 2), (4, 2), (4, 3);
a = [1, 2, 4, 3], inversion: (4, 3);
a = [1, 4, 2, 3], inversions: (3, 2), (4, 2).

Informação

Provedor Codeforces

Código CF911D