Problem Statement

There are N stones placed on a 2-dimensional plane. The i-th stone is located at coordinates (X_i, Y_i). All stones are located at lattice points in the first quadrant (including the axes).
Count the number of lattice points (x, y) where no stone is placed and it is impossible to reach (-1, -1) from (x, y) by repeatedly moving up, down, left, or right by 1 without passing through coordinates where a stone is placed.
More precisely, count the number of lattice points (x, y) where no stone is placed, and there does not exist a finite sequence of integer pairs $(x_0, y_0), \ldots, (x_k, y_k)$ that satisfies all of the following four conditions:

• (x_0, y_0) = (x, y).
• (x_k, y_k) = (-1, -1).
• |x_i - x_{i+1}| + |y_i - y_{i+1}| = 1 for all $0 \leq i < k$.
• There is no stone at (x_i, y_i) for all $0 \leq i \leq k$.

Input

The input is given from Standard Input in the following format:
N
X_1 Y_1
$\vdots$
X_N Y_N

Output

Print the number of lattice points that satisfy the conditions.

Constraints

• $0 \leq N \leq 2 \times 10^5$
• $0 \leq X_i, Y_i \leq 2 \times 10^5$
• The pairs (X_i, Y_i) are distinct.
• All input values are integers.

Sample Input 1

5
1 0
0 1
2 3
1 2
2 1

Sample Output 1

1

It is impossible to reach (-1, -1) from (1, 1).

Sample Input 2

0

Sample Output 2

0

There may be cases where no stones are placed.

Sample Input 3

22
0 1
0 2
0 3
1 0
1 4
2 0
2 2
2 4
3 0
3 1
3 2
3 4
5 1
5 2
5 3
6 0
6 4
7 0
7 4
8 1
8 2
8 3

Sample Output 3

6

There are six such points: (6, 1), (6, 2), (6, 3), (7, 1), (7, 2), (7, 3).

见题面 Input 部分

见题面 Output 部分