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 $0 \leq i \leq k$.

The input is given from Standard Input in the following format:

```
$N$
$X_1$ $Y_1$
$\vdots$
$X_N$ $Y_N$
```

Print the number of lattice points that satisfy the conditions.

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

1

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

0

There may be cases where no stones are placed.

6

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