For an empty set $S$, given $q$ queries, where each query is an integer $x$:
- `1 x a`: Insert $a$ elements with value $x$ into the set.
- `2 x b`: Remove $b$ elements with value $x$ from the set. If the number of elements with value $x$ in the set is less than $b$, remove all elements with value $x$.
- `3`: Find the minimum value in the set.
- `4`: Find the maximum value in the set.
- `5 y`: Let $x$ be the maximum value less than $y$ in the set, and $z$ be the minimum value greater than $y$ in the set. Calculate the sum of elements with values $x$ or $y$ or $z$. If there is no satisfied $x,y$ or $z$, you can ignore them.
The set $S$ may contain multiple elements with the same value.
### Input
- The first line contains an integer $q$.
- The next $q$ lines, each containing a query in the specified format.
### Output
- For each query of types $3,4,5$, print an integer as the answer.
### Constraints
- $1 \le q \le 10^5$.
- $1 \le x, a, b, y \le 10^6$.
### Example
Input
```
8
1 1 3
1 2 2
5 1
3
2 1 2
1 3 4
4
5 2
```
Output:
```
7
1
3
17
```
