In this problem, you have to maintain a dynamic set of numbers which support the two fundamental operations

• INSERT(S,x): if x is not in S, insert x into S
• DELETE(S,x): if x is in S, delete x from S

and the two type of queries

• K-TH(S) : return the k-th smallest element of S
• COUNT(S,x): return the number of elements of S smaller than x

Input

• Line 1: Q (1 ≤ Q ≤ 200000), the number of operations
• In the next Q lines, the first token of each line is a character I, D, K or C meaning that the corresponding operation is INSERT, DELETE, K-TH or COUNT, respectively, following by a whitespace and an integer which is the parameter for that operation.

If the parameter is a value x, it is guaranteed that 0 ≤ |x| ≤ 10⁹. If the parameter is an index k, it is guaranteed that 1 ≤ k ≤ 10⁹.

Output

For each query, print the corresponding result in a single line. In particular, for the queries K-TH, if k is larger than the number of elements in S, print the word 'invalid'.

Example

Input
8
I -1
I -1
I 2
C 0
K 2
D -1
K 1
K 2
Output
1
2
2
invalid