AT_arc205_c [ARC205C] No Collision Moves

There are $ N $ people on a number line. Person $ i $ $ (1\le i\le N) $ is initially at coordinate $ S_i $ , and wants to eventually move to coordinate $ T_i $ . It is guaranteed that $ S_1,S_2,\ldots,S_N,T_1,T_2,\ldots,T_N $ are all distinct. You fix one permutation $ P=(P_1,P_2,\ldots,P_N) $ of $ (1,2,\ldots,N) $ and perform $ N $ operations in order. In the $ i $ -th operation $ (1\le i\le N) $ , you move person $ P_i $ from coordinate $ S_{P_i} $ to coordinate $ T_{P_i} $ along the shortest path on the number line. However, if there is another person on the movement path, a fight occurs. Determine if there exists a $ P $ such that no fight occurs, and if it exists, find one.

The input is given from Standard Input in the following format: > $ N $ $ S_1 $ $ T_1 $ $ S_2 $ $ T_2 $ $ \vdots $ $ S_N $ $ T_N $

If there is no $ P $ such that no fight occurs, output `No`. Otherwise, output a $ P $ such that no fight occurs in the following format. > Yes $ P_1 $ $ P_2 $ $ \ldots $ $ P_N $ If there are multiple $ P $ that satisfy the condition, any of them will be accepted.

### Sample Explanation 1 If $ P=(3,2,1,4) $ , then the $ N $ operations proceed as follows. - $ 1 $ st operation: Move person $ 3 $ from coordinate $ 7 $ to coordinate $ 5 $ . The other three people are at coordinates $ 1,2,8 $ , so no fight occurs. - $ 2 $ nd operation: Move person $ 2 $ from coordinate $ 2 $ to coordinate $ 4 $ . The other three people are at coordinates $ 1,5,8 $ , so no fight occurs. - $ 3 $ rd operation: Move person $ 1 $ from coordinate $ 1 $ to coordinate $ 3 $ . The other three people are at coordinates $ 4,5,8 $ , so no fight occurs. - $ 4 $ th operation: Move person $ 4 $ from coordinate $ 8 $ to coordinate $ 10 $ . The other three people are at coordinates $ 3,4,5 $ , so no fight occurs. Therefore, outputting $ P=(3,2,1,4) $ will be accepted. Other acceptable outputs include $ P=(4,3,2,1),(2,1,3,4) $ . ### Sample Explanation 2 There is no $ P $ such that no fight occurs. Therefore, output `No`. ### Constraints - $ 1\le N\le 2\times 10^5 $ - $ 1\le S_i, T_i \le 10^9 $ - $ S_1,S_2,\ldots,S_N,T_1,T_2,\ldots,T_N $ are all distinct. - All input values are integers.