Zhily and Jily enjoy jumping around on a sequence. They move according to some rule, and throughout the process, they draw energy from the interval corresponding to their current positions. They use this energy to restore logical stability. You are given two permutations(^{\text{∗}}) (a) and (b) of length (n). For any open interval (I = (l, r)) where (0 \le l \lt r \le n+1) and (l + 1 \lt r) holds, we define (\operatorname{next}(I) = (\min(i, j), \max(i,j))), where (i = \operatorname*{argmax}\limits_{k \in (l, r)} a_k)(^{\text{†}}); (j = \operatorname*{argmax}\limits_{k \in (l, r)} b_k). You are also given a (0)-indexed non-negative sequence (p) of length (n). The sequence (g(I)) is defined as (g(I) = \begin{cases} 0 & (p_l = 0) \\ 1^{p_l} & (p_l \gt 0) \end{cases})(^{\text{‡}}). The sequence (f(I, k)) is defined as (f(I, k) = \begin{cases} ~ & \text{if } k=0 \text{ or } l+1\ge r \\ g(I) + f(\operatorname{next}(I), k-1) & \text{otherwise} \end{cases})(^{\text{§}}). You need to perform (m) operations: 1 l r k : Output the maximum number of consecutive (1)s in (f((l, r), k)). 2 x y : Assign (y) to (p_x). (^{\text{∗}})A permutation of length (n) is an array consisting of (n) distinct integers from (1) to (n) in arbitrary order. For example, (2,3,1,5,4) is a permutation, but (1,2,2) is not a permutation ((2) appears twice in the array), and (1,3,4) is also not a permutation ((n=3) but there is (4) in the array). (^{\text{†}})(\operatorname*{argmax}\limits_{k \in (l, r)}) (a_k) denotes the unique index (k) ((l \lt k \lt r)) such that (a_k = \max\limits_{x \in (l, r)} a_x). (^{\text{‡}})Here, (1^m) represents a sequence of length (m) consisting of all (1)s. (^{\text{§}})Here, (~) represents the empty sequence, and the operator (+) between two sequences i