Song List

Given a list of songs, calculate the minimal number of keys a user has to press to move the cursor from a certain song to another.

There are 3 keys with different functions: "previous", "next" and "sort". When the "previous" key is pressed, the cursor moves to the previous song, if it's already at the first song, it goes to the last one. The "next" key works analogously. When the "sort" key is pressed, the list is sorted alphabetically. Each song has it's title and author, if the "sort" key is pressed when the list is sorted by title, it sorts the list by author, and vice versa. After sorting, the cursor stays at the same song.


The input contains several cases. Each case begins with three positive integers: n, the number of songs(at most 10000), s and f, the initial and final position of the cursor(1 <= s, f <= n). Then n lines follow, each contains two strings with no more than 10 characters each, which are the title and the author of that song. The titles and authors are unique. Songs are initially sorted by title.


For each case,output the minimal number of keys one has to press to move the cursor from its initial position to the final position.

Sample Input

6 1 4
a a
b c
c d
d b
e e
f f

Sample Output



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