Berland is facing dark times again. The army of evil lord Van de Mart is going to conquer the whole kingdom. To the council of war called by the Berland's king Valery the Severe came n knights. After long discussions it became clear that the kingdom has exactly n control points (if the enemy conquers at least one of these points, the war is lost) and each knight will occupy one of these points.

Berland 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, b_i. For each pair you have to find out: how many fences a knight from control point with index a_i has to climb over to reach control point b_i (in case when Van de Mart attacks control point b_i first). As each knight rides a horse (it is very difficult to throw a horse over a fence), you are to find out for each pair the minimum amount of fences to climb over.

Input

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 Kx_i, Ky_i ( - 10⁹ ≤ Kx_i, Ky_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, Cx_i, Cy_i (1 ≤ r_i ≤ 10⁹, - 10⁹ ≤ Cx_i, Cy_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

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

Knights

Examples