AT_past19_f ドミノ倒し

You are lining up dominoes. $ N $ clues are given: for each $ 1 \leq i \leq N $ , if domino $ S_i $ falls, then domino $ T_i $ will also fall. Determine if the given clues imply that if domino $ X $ falls, then domino $ Y $ will also fall.

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

Print `Yes` if the given clues imply that if domino $ X $ falls, then domino $ Y $ will also fall; print `No` otherwise.

### Sample Explanation 1 The second clue states that if domino `second` falls, then domino `third` will also fall; and the third clue states that if domino `third` falls, then domino `fourth` will also fall. Thus, we can infer that if domino `second` falls, then domino `fourth` will also fall. ### Sample Explanation 2 One cannot infer from the given clues that if domino `fourth` falls, then domino `second` will also fall. ### Constraints - $ 1 \leq N \leq 2\times 10^5 $ - $ N $ is an integer. - Each of $ S_i,T_i,X $ , and $ Y $ is a string of length between $ 1 $ and $ 100 $ , inclusive, consisting of lowercase English letters. - $ X \neq Y $ - $ S_i \neq T_i $ for all $ i $ . - $ (S_i,T_i) $ are distinct.