Description

Determine the positional relationship between a point and a given triangle.

Input Format

• The first three lines, each contains a coordinate, representing the three vertices of the triangle.
• The fourth line contains the coordinate of a point. Determine the positional relationship between this point and the triangle formed by the previous three points.
• All coordinate values are integers.

Output Format

• If the point is inside the triangle (excluding the boundary), output $1$.
• If the point is outside the triangle (excluding the boundary), output $2$.
• If the point is on the boundary of the triangle (excluding vertices), output $3$.
• If the point is on a vertex of the triangle, output $4$.

(0,0)
(3,0)
(0,3)
(1,1)

1

Hint

Constraints

For $100\%$ testdata, $0 \le x_i, y_i \le 100$.

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