White Rabbit is a businessman. It has n warehouses. The i-th warehouse is located at (x1[i],y1[i]) and has a[i] units of products initially.
There will be m orders coming in order.
When the i-th order is coming, White Rabbit will drive to s[i] warehouses from x[i][0] to x[i][S[i]-1] in order.
More specifically, White Rabbit will drive to the x[i][0]-th warehouse first(the car is empty before arriving at x[i][0]-th warehouse), and move any number of products to the car.
Then White Rabbit will drive to the x[i][1]-th warehouse. When arriving at x[i][1]-th warehouse, White Rabbit can put any number of products form the warehouse on the car or from the car on the warehouse.
After leaving the x[i][s[i]-1]-th warehouse, White Rabbit will go to the house of the customer and sell all of the rest products in the car to the customer. The house of i-th customer is located at (x2[i],y2[i]).
Besides, the i-th customer has a limit lim[i], denoting that the number of products White Rabbit gives the i-th customer can't be larger than lim[i].
White Rabbit wants to maximize the number of products it sells.
White Cloud wants to interfere White Rabbit. White Cloud has installed k Jammers. The i-th Jammer is located at (x3[i],y3[i]). It works on a circle with radius r[i]. If the connecting segments of two points are tangent or intersecting with the circle, the contact of two points will be disturbed.
To keep contact with the i-th customer, White Rabbit will skip x[i][t]-th(0<=t<S[i]) warehouse if the x[i][t]-th warehouse can't contact the house of i-th customer.
White Rabbit wants to know the maximum number of products it can sell.

The first line of input contains 3 integers n,m,k(n <= 1000,m <= 1000,k <= 10).
For the next n lines, each line contains 3 integers x1[i],y1[i],a[i].
For the next k lines, each line contains 3 integers x3[i],y3[i],r[i].
For the next m lines, the i-th line contains 4+s[i] integers x2[i],y2[i],s[i],lim[i] and s[i] different numbers.
All the number in input is in range [0,1000000000].
The input ensure that the location of customers' homes and warehouses is not within the coverage of any jammer.

Print the maximum number of products White Rabbit can sell.

3 3 1
1 1 5
4 5 0
9 2 7
2 2 1
4 4 2 3 1 2
0 9 2 3 1 2
9 1 2 8 3 2

11