In this problem you will be given a set of points in the Eu- clidian plane. The number of points in the set will never exceed 100000. The coordinates of these points will be in- teger coordinates and will have an absolute value smaller than 10000. There will be no identical points in the first set. Then you will be given a second set of points. For each point in the second set you will have to determine whether it lies in a triangle spanned by three points in the first set. A point lying on the edge of a triangle is considered to be “inside” the triangle. In the example on the right the points p1, p2, p3, p4 be- long to the first set. The points r and s belong to the second set. The point r isn’t contained in any triangle spanned by three points of the first set. The point s is contained in two triangles. For example, the triangle spanned by p2, p3, p4. Input You will be given several testcases. A testcases consists of the number of points p, 3 ≤ p ≤ 100000 in the first set. It is followed by p pairs of numbers, each describing a point of the first set, the first number of a pair denoting the x-coordinate of the point, the second the y-coordinate. Each pair is on a seperate line. There may be colinear points in the first set. The next number in the input gives you the number of points r in the second set. It is followed by r pairs of numbers, each describing a point, each on a separate line. The first number of a pair being the x-coordinate, the second number being the y-coordinate of the point. All coordinates in the input will be integer coordinates. Output For each point in the second set, output if the point lies in a triangle spanned by three points of the first set. If the point lies inside a triangle output ‘inside’ otherwise output ‘outside’. Sample Input 4 00 44 04 40 6 22 44 11 02 0 10 10 0
2/2 Sample Output inside inside inside inside outside outside