**Time limit:**1.00 s**Memory limit:**512 MB

The polygon consists of $n$ vertices $(x_1,y_1),(x_2,y_2),\dots,(x_n,y_n)$. The vertices $(x_i,y_i)$ and $(x_{i+1},y_{i+1})$ are adjacent for $i=1,2,\dots,n-1$, and the vertices $(x_1,y_1)$ and $(x_n,y_n)$ are also adjacent.

**Input**

The first input line has an integer $n$: the number of vertices.

After this, there are $n$ lines that describe the vertices. The $i$th such line has two integers $x_i$ and $y_i$.

You may assume that the polygon is simple, i.e., it does not intersect itself.

**Output**

Print two integers: the number of lattice points inside the polygon and on its boundary.

**Constraints**

- $3 \le n \le 10^5$

- $-10^6 \le x_i, y_i \le 10^6$

**Example**

Input:

`4`

1 1

5 3

3 5

1 4

Output:

`6 8`