AT_aalc001_f 連

You are given a sequence of nonnegative integers $ A=(A_1,A_2,\ldots,A_N) $ of length $ N $ . Process $ Q $ queries. Each query is of one of the following $ 2 $ types: - `1 i x`: Change $ A_i $ to $ x $ . - `2 l r`: Print the largest positive integer $ k $ satisfying the following condition: - There exists an integer $ p $ such that $ l \leq p \leq p+k-1 \leq r $ and $ A_p=A_{p+1}=\cdots=A_{p+k-1} $ .

The input is given from Standard Input in the following format: > $ N $ $ Q $ $ A_1 $ $ A_2 $ $ \ldots $ $ A_N $ $ \mathrm{query}_1 $ $ \mathrm{query}_2 $ $ \vdots $ $ \mathrm{query}_Q $ Each query is given in one of the following formats: > $ 1 $ $ i $ $ x $ > $ 2 $ $ l $ $ r $

Let $ q $ be the number of type $ 2 $ queries. Print $ q $ lines. The $ j $ -th line should contain the answer to the $ j $ -th type $ 2 $ query.

### Sample Explanation 1 The answers to the first $ 2 $ queries are $ 3,2 $ , respectively. After processing query $ 3 $ , $ A=(1,1,2,2,2,2,2,2) $ , so the answer to the next query is $ 6 $ . ### Constraints - $ 1 \leq N \leq 2 \times 10^5 $ - $ 1 \leq Q \leq 2 \times 10^5 $ - $ 0 \leq A_i \leq 10^9 $ - For type $ 1 $ queries, $ 1 \leq i \leq N $ , $ 0 \leq x \leq 10^9 $ - For type $ 2 $ queries, $ 1 \leq l \leq r \leq N $ - All numerical values in the input are integers.