Chef likes trees a lot. Today he has an infinte full binary tree (each node has exactly two childs) with special properties.
Chef's tree has the following special properties :

Each node of the tree is either colored red or black.
Root of the tree is black intially.
Both childs of a red colored node are black and both childs of a black colored node are red.

The root of the tree is labelled as 1. For a node labelled v, it's left child is labelled as 2v and it's right child is labelled as 2v+1.

Chef wants to fulfill Q queries on this tree. Each query belongs to any of the following three types:

Qi Change color of all red colored nodes to black and all black colored nodes to red.
Qb x y Count the number of black colored nodes on the path from node x to node y (both inclusive).
Qr x y Count the number of red colored nodes on the path from node x to node y (both inclusive).

Help chef accomplishing this task.

Input
First line of the input contains an integer Q denoting the number of queries. Next Q lines of the input contain Q queries (one per line). Each query belongs to one of the three types mentioned above.

Output
For each query of type Qb or Qr, print the required answer.

Constraints

1<=Q<=10^5

1<=x,y<=10^9

Sample Input
5
Qb 4 5
Qr 4 5
Qi
Qb 4 5
Qr 4 5

Sample Output
2
1
1
2

Explanation
With the initial configuration of the tree, Path from node 4 to node 5 is 4->2->5 and color of nodes on the path is B->R->B.

Number of black nodes are 2.
Number of red nodes are 1.

After Query Qi, New configuration of the path from node 4 to node 5 is R->B->R.

Number of black nodes are 1.
Number of red nodes are 2.

Scoring

Subtask #1: 1<=Q<=100 1<=x,y<=1000   : 27 pts
Subtask #2: 1<=Q<=10^3 1<=x,y<=10^5     :  25 pts

Subtask #3: 1<=Q<=10^5 1<=x,y<=10^9     :  48 pts

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