## ORDERSET - Order statistic set

English | Vietnamese |

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| ≤ 10^{9}. If the parameter is an index k, it is guaranteed that 1 ≤ k ≤ 10^{9}.

### 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

Input8 I -1 I -1 I 2 C 0 K 2 D -1 K 1 K 2Output1 2 2 invalid

Added by: | Jimmy |

Date: | 2008-10-28 |

Time limit: | 1.5s-2s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All except: ERL JS-RHINO NODEJS PERL6 VB.NET |

Resource: | Chess |