Chaotic Sequence

10 students are standing in a row. From left to right, they are labeled as 1 to 10. When the teacher left for the bathroom, they start to switch positions. When the teacher come back on the \(k^\text{th}\) minute, the queue becomes the \(k^\text{th}\) lexicography order.

The teacher needs your help to answer 2 types of queries:

  • K L N : On the \(k^\text{th}\) minute, what is the label of the \(n^\text{th}\) person from the left?
  • K P N : On the \(k^\text{th}\) minute, what is the position of the person labeled \(n\)?

This file contains 1000 queries. What is the sum of all output?

Sample Input

1
2
3
4
5
6
7
8
1 L 1
1 L 2
1 L 10
2 L 10
1 P 1
1 P 2
1 P 10
2 P 9

Sample Output

1
2
3
4
5
6
7
8
1
2
10
9
1
2
10
10

For this example, the answer is 45.

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