AT_arc203_b [ARC203B] Swap If Equal Sum

You are given length- $ N $ integer sequences $ A=(A_1,A_2,\dots,A_N) $ and $ B=(B_1,B_2,\dots,B_N) $ , each consisting of $ 0 $ and $ 1 $ . Let $ A[i,j] $ denote the consecutive subsequence of $ A $ from the $ i $ -th through the $ j $ -th element. If $ i>j $ , then $ A[i,j] $ is a length- $ 0 $ sequence. You can perform the following operation on $ A $ any number of times: - Choose four integers $ a,b,c,d $ that satisfy the following two conditions: - $ 1 \leq a \leq b < c \leq d \leq N $ - $ \sum_{i=a}^{b}{A_i}=\sum_{i=c}^{d}{A_i} $ - Swap $ A[a,b] $ and $ A[c,d] $ . More precisely, replace $ A $ with the sequence formed by concatenating $ A[1,a-1] $ , $ A[c,d] $ , $ A[b+1,c-1] $ , $ A[a,b] $ , $ A[d+1,N] $ in this order. Determine whether $ A $ can be made to match $ B $ . Solve $ T $ test cases for each input file.

The input is given from Standard Input in the following format: > $ T $ $ case_1 $ $ case_2 $ $ \vdots $ $ case_T $ Each case is given in the following format: > $ N $ $ A_1 $ $ A_2 $ $ \dots $ $ A_N $ $ B_1 $ $ B_2 $ $ \dots $ $ B_N $

Output the answers in a total of $ T $ lines. The $ t $ -th line should contain `Yes` if $ A $ can be made to match $ B $ for the $ t $ -th test case, and `No` otherwise.

### Sample Explanation 1 In the first test case, $ A $ is initially $ (1,1,1,0,0,1) $ . By choosing $ (a,b,c,d)=(1,2,3,6) $ and performing the operation, $ A $ becomes $ (1,0,0,1,1,1) $ . Next, by choosing $ (a,b,c,d)=(1,2,3,4) $ and performing the operation, $ A $ becomes $ (0,1,1,0,1,1) $ , which matches $ B $ . In the second test case, $ A $ cannot be made to match $ B $ . In the third test case, $ A $ already matches $ B $ from the beginning. ### Constraints - $ 1 \leq T \leq 10^5 $ - $ 2 \leq N \leq 2 \times 10^5 $ - $ 0 \leq A_i \leq 1 $ - $ 0 \leq B_i \leq 1 $ - The sum of $ N $ over all test cases is at most $ 2\times 10^5 $ . - All input values are integers.