A15152 | Rooks Defenders

You have a square chessboard of size $n \times n$ . Rows are numbered from top to bottom with numbers from $1$ to $n$ , and columns — from left to right with numbers from $1$ to $n$ . So, each cell is denoted with pair of integers $(x, y)$ ( $1 \le x, y \le n$ ), where $x$ is a row number and $y$ is a column number.

You have to perform $q$ queries of three types:

- Put a new rook in cell $(x, y)$ .
- Remove a rook from cell $(x, y)$ . It's guaranteed that the rook was put in this cell before.
- Check if each cell of subrectangle $(x_1, y_1) - (x_2, y_2)$ of the board is attacked by at least one rook.

Subrectangle is a set of cells $(x, y)$ such that for each cell two conditions are satisfied: $x_1 \le x \le x_2$ and $y_1 \le y \le y_2$ .

Recall that cell $(a, b)$ is attacked by a rook placed in cell $(c, d)$ if either $a = c$ or $b = d$ . In particular, the cell containing a rook is attacked by this rook.

The first line contains two integers $n$ and $q$ ( $1 \le n \le 10^5$ , $1 \le q \le 2 \cdot 10^5$ ) — the size of the chessboard and the number of queries, respectively.

Each of the following $q$ lines contains description of a query. Description begins with integer $t$ ( $t \in \{1, 2, 3\}$ ) which denotes type of a query:

- If $t = 1$ , two integers $x$ and $y$ follows ( $1 \le x, y \le n$ ) — coordinated of the cell where the new rook should be put in. It's guaranteed that there is no rook in the cell $(x, y)$ at the moment of the given query.
- If $t = 2$ , two integers $x$ and $y$ follows ( $1 \le x, y \le n$ ) — coordinates of the cell to remove a rook from. It's guaranteed that there is a rook in the cell $(x, y)$ at the moment of the given query.
- If $t = 3$ , four integers $x_1, y_1, x_2$ and $y_2$ follows ( $1 \le x_1 \le x_2 \le n$ , $1 \le y_1 \le y_2 \le n$ ) — subrectangle to check if each cell of it is attacked by at least one rook.

It's guaranteed that among $q$ queries there is at least one query of the third type.

Print the answer for each query of the third type in a separate line. Print "Yes" (without quotes) if each cell of the subrectangle is attacked by at least one rook.

Otherwise print "No" (without quotes).