Problem Description

In $2026$, “computing-power and electricity coordination” was written into the government work report for the first time, and together with ultra-large-scale intelligent computing clusters, it was listed as a national-level new infrastructure project, supporting the construction of a nationwide integrated computing-power scheduling system. During the project implementation, national computing-power hub nodes need to manage a large number of computing units in real time.

Each computing unit has an energy-efficiency value $v$ in the form of a non-negative integer. To optimize energy scheduling, the scheduling system needs to count the number of pairs of units that satisfy the “coordination condition”. Define two computing units $(i, j)$ as a coordinated pair if and only if:

• $i < j$;
• $\text{Fib}(v_i + v_j) = \text{Fib}(v_i) + \text{Fib}(v_j)$.

Here, $\text{Fib}(x)$ denotes the $x$-th Fibonacci number. The Fibonacci sequence is defined as follows:

• $\text{Fib}(0) = 0$;
• $\text{Fib}(1) = 1$;
• For $x \ge 2$, $\text{Fib}(x) = \text{Fib}(x-1) + \text{Fib}(x-2)$.

Now, you need to maintain an initially empty pool of computing units and process $q$ operations:

• $1\ k\ v$: Add $k$ computing units with energy-efficiency value $v$.
• $2\ k\ v$: Remove at most $k$ computing units with energy-efficiency value $v$. If there are fewer than $k$ units with value $v$, remove all of them.
• $3$: Query how many coordinated pairs of units there are in total at the moment.

Please write a program to simulate the operation of this scheduling system and output the corresponding result for each query.

Input Format

The first line contains a positive integer $q$, indicating the number of operations.
The next $q$ lines each describe one operation:

• $1\ k\ v$: Add $k$ units with value $v$.
• $2\ k\ v$: Remove at most $k$ units with value $v$.
• $3$: Query the current total number of coordinated pairs.

Output Format

For each operation $3$, output one line containing one integer, indicating the current total number of coordinated pairs.

5
1 2 0
1 3 1
3
2 4 0
3

7
0

Hint

Constraints and Notes

For $30\%$ of the testdata, $1 \le q \le 10^3$, $1 \le k \le 10$.

For all testdata, $1 \le q \le 2 \times 10^5$, $0 \le v \le 10^9$, $1 \le k \le 10^3$.

Translated by ChatGPT 5