Note: This is the harder version of Chapter 1. This version involves an array of integers instead of a string, and the array may change with updates.

An array is perfectly balanced if its length is even, and the first half of the array can be shuffled to make the array a palindrome. For example, ([15,2,15,2]) and ([7,5,5,7]) are perfectly balanced, but ([7,5,3,1,3,5,7]) and ([3,1,1,3,2,3]) are not.

An array is almost perfectly balanced if you can delete exactly one element from it to make it perfectly balanced. Some examples are ([1, 2, 3, 4, 4, 5, 1, 3, 2]), ([1]), and ([2, 2, 2, 3, 2]).

You are given a larger template array (A_1 ... A_N) of length (N), along with (Q) events, the (i)th of which is one of the following two formats:

(1) (X_i) (Y_i): set (A_{X_i}) to (Y_i).
(2) (L_i) (R_i): check whether the subarray (A_{L_i..R_i}) is almost perfectly balanced.

For how many type-2 queries is the subarray almost perfectly balanced?

Constraints

(1 \le T \le 85) (1 \le N \le 10^6) (1 \le A_i \le 10^6) (1 \le Q \le 10^6) (1 \le X_i \le N) (1 \le Y_i \le 10^6) (1 \le L_i \le R_i \le N)

The sum of (N) across all test cases is at most (4{,}000{,}000). The sum of (Q) across all test cases is at most (4{,}000{,}000).

Input Format

Input begins with a single integer (T), the number of test cases. For each test case, there is first a line containing a single integer (N). Then, there is a line containing (N) space-separated integers (A_1, ..., A_N). Then, there is a line containing a single integer (Q). Then, (Q) lines follow, the (i)th of which contains three space-separated integers, either "(1) (X_i) (Y_i)" or "(2) (L_i) (R_i)".

Output Format

For the (i)th test case, output a single line containing "Case #i: ", followed by a single integer: the number of queries which are an almost perfectly balanced subarray.

Sample Explanation

In the first case, the template array is ([2,1,5,1,5,1]).

For the first query, the subarray is ([1,5,1,5,1]). You can delete the second (1) to get ([1,5,5,1]), which is a palindrome. Thus, ([1,5,1,5,1]) is an almost perfectly balanced subarray.

For the second query, the subarray is ([2,1,5,1,5]). You can delete the (2) to get ([1,5,1,5]) then reorder the first half of the array to get ([5,1,1,5]), which is a palindrome. Thus, ([2,1,5,1,5]) is an almost perfectly balanced subarray.

For the third query, the subarray is ([2,1,5]). You cannot delete any element to get an almost perfectly balanced subarray.

The next two events are updates, after which the template array is ([5, 5, 5, 1, 5, 1]).

For the fourth query, the subarray is ([5,5,5]). You can delete any element to get ([5,5]), which is a palindrome. Thus, ([5,5,5]) is an almost perfectly balanced subarray.

The fifth, sixth, eighth, and tenth queries are also almost perfectly balanced subarrays, so the final answer is (7).