ORDERSET - Order statistic set


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

hide comments
hitman007: 2018-01-21 20:22:58

Any Java programmer here who got it accepted ? I am hearing only c++programs. In Java, even with Compression + BIT + Binary search + Fast I/O, I am getting TLE after test case #6.

hitman007: 2018-01-21 16:58:07

Implemented with BIT. But constantly getting WA after test case #5. Any hint ?

be1035016: 2017-12-29 16:57:27

map with bit->0.56sec
unordered_map with bit->0.45sec

pranavraj219: 2017-12-13 22:51:51

BIT - 0.35s
SEGTREE - 0.75s
Regular map did not give TLE but still its better to use unordered_map.

sarwar__05: 2017-12-10 00:08:14

TLE with std::map, AC with std::unordered_map

amulyagaur: 2017-10-20 07:06:57

Direct implementation of policy based data structures in C++

shubham_7616: 2017-08-17 22:08:43

Just loved it......Learned a lot !!
Nice application of BIT.
For those getting TLE use unordered map instead of map and use scanf printf .

starbot: 2017-08-17 20:19:00

Amazing problem...learnt a lot...time to play cs

fz0718: 2017-07-25 04:34:21

The four magic lines of code... :)

#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;

akt_1998: 2017-07-03 11:29:26

Must do question for beginners in BIT


Added by:Duc
Date:2008-10-28
Time limit:0.300s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:© VNOI