Order Statistic Set Operations

You are required to implement a data structure to maintain a set of integers (each with absolute value at most $10^9$). Initially, the set is empty. You need to support the following operations (with at most $10^4$ operations in total):

1. Given an integer $x$, report its rank, defined as the number of elements in the set strictly less than $x$, plus one. (Note that $x$ may not be present in the set.)
2. Query the element with rank $x$ ($x\ge 1$). It is guaranteed that there are at least $x$ elements in the set.
3. Find the predecessor of $x$ in the set (i.e. the largest number in the set that is strictly less than $x$). If no such number exists, output $-2147483647$.
4. Find the successor of $x$ in the set (i.e. the smallest number in the set that is strictly greater than $x$). If no such number exists, output $2147483647$.
5. Insert the integer $x$ into the set. It is guaranteed that $x$ is not present in the set before insertion.

It is guaranteed that for operations 1, 3 and 4 the set is non-empty when the operation is executed.

inputFormat

The first line contains an integer $q$ ($1\le q\le 10^4$), the number of operations. Each of the following $q$ lines contains two integers $op$ and $x$, where:

• If $op = 1$, you should output the rank of $x$.
• If $op = 2$, you should output the element whose rank is $x$.
• If $op = 3$, you should output the predecessor of $x$.
• If $op = 4$, you should output the successor of $x$.
• If $op = 5$, you should insert $x$ into the set.

outputFormat

For each query operation (operations 1, 2, 3, and 4), output the result on a new line.

sample

5
5 10
5 20
1 10
3 20
4 10

1
10
20