Description

On an infinite chessboard, there are $n$ distinct pieces at positions $(x_i, y_i)$. You must delete all pieces by performing the following operation multiple times:

1. Choose a grid $(x, y)$.
2. If there is a piece at $(x, y)$, delete it. Otherwise, end the current operation.
3. Sequentially check the grids at $(x+1, y+1)$, $(x+1, y)$, and $(x+1, y-1)$. Upon finding the first grid with a piece, stop checking, update $(x, y)$ to this grid's coordinates, and return to Step 2. If none of these grids contain a piece, end the current operation.

Determine the minimum number of operations required to delete all pieces.

Input Format

The first line contains a positive integer $n$ indicating the number of pieces.

The next $n$ lines each contain two positive integers $x_i$, $y_i$ representing the coordinates of a piece. All positions are guaranteed to be distinct.

Output Format

Output a single positive integer representing the minimum number of operations needed.

4
1 3
2 2
3 1
3 3

2

9
1 1
1 2
1 3
2 1
2 2
2 3
3 1
3 2
3 3

3

Hint

Explanation #1

For the first sample, the chessboard is shown below:

• First operation: Choose $(1, 3)$. This deletes the pieces at $(1, 3)$, $(2, 2)$, and $(3, 3)$.
• Second operation: Choose $(3, 1)$. This deletes the piece at $(3, 1)$.

It can be proven that no better strategy exists.

Constraints

This problem uses subtask scoring.

For all test data: $1 \le n \le 10^6$, $1 \le x_i, y_i \le 10^6$.

• Special Property A: All $x_i$ are equal.

Translated by DeepSeek R1