AT_aalc001_r 連結性

There is a grid with $ N $ rows and $ W $ columns. Let cell $ (i,j) $ denote the cell in the $ i $ -th row from the top and the $ j $ -th column from the left. Each cell of the grid contains $ 1 $ digit. Initially, cell $ (i,j) $ contains the $ j $ -th character of the string $ S_i $ . Process $ Q $ queries. Each query is of one of the following $ 2 $ types: - `1 i T`: For $ j=1,2,\ldots,W $ , change the digit in cell $ (i,j) $ to the $ j $ -th character of $ T $ . - `2 a b c d`: Determine whether you can reach cell $ (c,d) $ from cell $ (a,b) $ by repeatedly moving to a cell that shares an edge with the current cell and contains the same digit as the current cell.

The input is given from Standard Input in the following format: > $ N $ $ W $ $ Q $ $ S_1 $ $ S_2 $ $ \vdots $ $ S_N $ $ \mathrm{query}_1 $ $ \mathrm{query}_2 $ $ \vdots $ $ \mathrm{query}_Q $ Each query is given in one of the following formats: > $ 1 $ $ i $ $ T $ > $ 2 $ $ a $ $ b $ $ c $ $ d $

Let $ q $ be the number of type $ 2 $ queries. Print $ q $ lines. On the $ j $ -th line, print `Yes` if the destination can be reached in the $ j $ -th type $ 2 $ query, and `No` otherwise.

### Sample Explanation 1 Initially, you can reach cell $ (2,5) $ from cell $ (1,1) $ by passing only through cells containing the digit $ 0 $ . However, you cannot reach cell $ (4,1) $ from cell $ (1,1) $ . After changing row $ 3 $ to `00000`, you can reach cell $ (4,1) $ from cell $ (1,1) $ . ### Sample Explanation 2 You can reach cell $ (3,7) $ from cell $ (4,1) $ by moving in the following order, for example: \\\[ (4,1),(3,1),(2,1),(1,1),(1,2),(1,3),(2,3),(3,3),(3,4),(3,5),(2,5),(1,5),(1,6),(1,7),(2,7),(3,7) \\\] ### Constraints - $ 2 \le N \le 10^5 $ - $ 2 \le W \le 10 $ - $ 1 \le Q \le 5 \times 10^4 $ - $ S_i $ is a string of length $ W $ consisting of digits. - For type $ 1 $ queries, $ 1 \le i \le N $ - For type $ 1 $ queries, $ T $ is a string of length $ W $ consisting of digits. - For type $ 2 $ queries, $ 1 \le a,c \le N $ , $ 1 \le b,d \le W $ - For type $ 2 $ queries, $ (a,b) \ne (c,d) $ - When a type $ 2 $ query is given, cells $ (a,b) $ and $ (c,d) $ contain the same digit. - All numerical values in the input are integers.