Given an empty sequence $S$, perform a series of $t$ operations, each belonging to one of the following types:
- Add an element $x$ to the end of sequence $S$.
- Calculate the sum of elements having values within the range $[a,b]$.
- Rearrange sequence $S$ in non-decreasing order, then calculate the sum of elements with indices from $p$ to $q$ (where $1 \le p \le q \le |S|$, and $|S|$ is the number of elements in sequence $S$). After that, append two elements to the end of sequence $S$: one with the value of the element at index $p$ plus $1$, and the other with the value of the element at index $q$ minus $1$.
### Input
- The first line consists of a positive integer $t$.
- The $i$-th line among the $t$ following lines describes the $i$-th operation, which is one of three types in the format: Start type $k$ ($k$ is either $1$ or $2$ or $3$). If it's operation type $1$, then it is followed by an integer $x$ ($−10^9 ≤ x ≤ 10^9$). If it's operation type $2$, then it is followed by two integers $a, b$ ($−10^9 ≤ a \le b ≤ 10^9$). If it's operation type $3$, then it is followed by two positive integers $p, q$.
### Output
- Print the answers for each operation of types $2$ and $3$.
### Constraints
- 40% of the tests have $t \le 1000$.
- 40% of the tests have $t \le 10^5$, with no operation of type $3$.
- 20% of the tests have $t \le 10^5$.
### Example
Input:
```
7
1 5
1 3
1 1
2 2 4
1 2
3 2 3
2 2 4
```
Output:
```
3
5
10
```
