Toyland is facing dark times again. The army of Gollies is going to invade Toyland. But Don't worry, Mr. Plod has come to the rescue with N policemen. After long discussions it became clear that the Toyland has exactly N control points (if the Gollies conquer at least one of these points, the war is lost) and each policeman will occupy one of these points.

Toyland is divided into M+1 regions with M fences, and the only way to get from one region to another is to climb over the fence. Each fence is a circle on a plane, no two fences have common points, and no control point is on the fence. You are given K pairs of numbers a_i and b_i. For each pair you have to find out: how many fences a policeman from control point with index a_i has to climb over to reach control point b_i (in case when the Gollies attack the control point b_i first). As each policeman rides a bicycle, All Policemen in Toyland have difficulty in climbing over fences, you are to find out for each pair the Minimum Amount of Fences to climb over.

Input Format
The first input line contains three integers N, M, K (1 <= N,M <= 1000, 0 <= K<= 100000).
Then follow N lines, each containing two integers x_i, y_i (-10⁹<= x_i,y_i<=10⁹) — coordinates of control point with index i. Control points can coincide.
Each of the following M lines describes fence with index i with three integers r_i, x_i, y_i (1 <= r_i <= 10⁹, -10⁹ <= x_i,y_i <= 10⁹ ) — radius and center of the circle where the corresponding fence is situated.

Then follow K pairs of integers a_i, b_i (1 <= a_i,b_i <= n), each in a separate line — requests that you have to answer. a_i and b_i can coincide.

Output Format
Output exactly K lines, each containing one integer — the answer to the corresponding request.