P6301 Set.

You need to maintain **online** a sorted set $S$ of natural numbers and support the following operations: 1. Given a number $x$, if $x$ is not in the set $S$, then insert $x$ into $S$. 2. Given a number $x$, if $x$ is already in the set $S$, then delete $x$ from $S$. To prove that you are maintaining $S$, you must answer the following queries during the operations: 3. Output the value of the minimum element in $S$. If $S=\varnothing$, return `-1`. 4. Output the value of the maximum element in $S$. If $S=\varnothing$, return `-1`. 5. Output the number of elements in $S$. 6. Given a number $x$, determine whether $x$ is in the set. If yes, return `1`; otherwise, return `0`. 7. Given a number $x$, let $T=S\cap[0^-,x)$. Output the value of the maximum element in $T$. If $T=\varnothing$, return `-1`. 8. Given a number $x$, let $T=S\cap[x,n)$. Output the value of the minimum element in $T$. If $T=\varnothing$, return `-1`. To prove that you maintain $S$ **online**, for all operations $1,2$ and queries $6,7,8$ after the first query, the actual parameter $x$ equals the parameter $x'$ given in the input plus the return value $\text{last}$ of the previous query. That is, $x=x'+\text{last}$. It is guaranteed that $0\le x

The input has $(m+1)$ lines, where the meaning of $m$ is given below. The first line contains two positive integers $n,m$, where $n$ is the upper bound of the parameter $x$ in operations and queries, and $m$ is the total number of operations and queries. The next $m$ lines each contain one or two natural numbers, representing one operation or one query. Each line is guaranteed to be in one of the following eight forms: 1. `1 x'`, meaning perform operation $1$. 2. `2 x'`, meaning perform operation $2$. 3. `3`, meaning answer query $3$. 4. `4`, meaning answer query $4$. 5. `5`, meaning answer query $5$. 6. `6 x'`, meaning answer query $6$. 7. `7 x'`, meaning answer query $7$. 8. `8 x'`, meaning answer query $8$.

To avoid too much output, you only need to output one line with one integer, which is the sum of the return values of all queries.

### Sample Explanation The operations actually performed and the queries actually answered are as follows: ```plain 1 0 1 1 1 3 1 3 3 -> 0 7 0 -> -1 7 1 -> 0 8 3 -> 3 4 -> 3 2 3 4 -> 1 6 3 -> 0 5 -> 2 ``` Therefore, the output is $0+(-1)+0+3+3+1+0+2=8$. ### Constraints | Test Point ID | $n=$ | $m=$ | Score | |:--------------:|:------------:|:-----------:|:-------:| | $1$ | $2^{20}$ | $2^{14}$ | $5$ | | $2$ | $2^{25}$ | $2^{17}$ | $5$ | | $3$ | $2^{30}$ | $2^{20}$ | $10$ | | $4$ | $2^{30}$ | $2^{22}$ | $15$ | | $5$ | $2^{30}$ | $2^{22}$ | $15$ | | $6$ | $2^{30}$ | $2^{23}$ | $25$ | | $7$ | $2^{30}$ | $2^{23}$ | $25$ | For $100\%$ of the testdata, $2^{20}\le n\le2^{30}$, $2^{14}\le m\le 2^{23}$, and $0\le x