Forbidden Value
Description
Polycarp is editing a complicated computer program. First, variable $x$ is declared and assigned to $0$. Then there are instructions of two types:
- set $y$ $v$ — assign $x$ a value $y$ or spend $v$ burles to remove that instruction (thus, not reassign $x$);
- if $y$ $\dots$ end block — execute instructions inside the if block if the value of $x$ is $y$ and ignore the block otherwise.
if blocks can contain set instructions and other if blocks inside them.
However, when the value of $x$ gets assigned to $s$, the computer breaks and immediately catches fire. Polycarp wants to prevent that from happening and spend as few burles as possible.
What is the minimum amount of burles he can spend on removing set instructions to never assign $x$ to $s$?
The first line contains two integers $n$ and $s$ ($1 \le n \le 2 \cdot 10^5$, $1 \le s \le 2 \cdot 10^5$) — the number of lines in the program and the forbidden value of $x$.
The following $n$ lines describe the program. Each line is one of three types:
- set $y$ $v$ $(0 \le y \le 2 \cdot 10^5, 1 \le v \le 10^9)$;
- if $y$ $(0 \le y \le 2 \cdot 10^5)$;
- end.
Each if instruction is matched by an end instruction. Each end instruction has an if instruction to match.
Print a single integer — the minimum amount of burles Polycarp can spend on removing set instructions to never assign $x$ to $s$.
Input
The first line contains two integers $n$ and $s$ ($1 \le n \le 2 \cdot 10^5$, $1 \le s \le 2 \cdot 10^5$) — the number of lines in the program and the forbidden value of $x$.
The following $n$ lines describe the program. Each line is one of three types:
- set $y$ $v$ $(0 \le y \le 2 \cdot 10^5, 1 \le v \le 10^9)$;
- if $y$ $(0 \le y \le 2 \cdot 10^5)$;
- end.
Each if instruction is matched by an end instruction. Each end instruction has an if instruction to match.
Output
Print a single integer — the minimum amount of burles Polycarp can spend on removing set instructions to never assign $x$ to $s$.
Samples
5 1
set 1 10
set 2 15
if 2
set 1 7
end
17
7 2
set 3 4
if 3
set 10 4
set 2 7
set 10 1
end
set 4 2
4
9 200
if 0
set 5 5
if 5
set 100 13
end
if 100
set 200 1
end
end
1
1 10
set 1 15
0