Nanami likes playing games, and is also really good at it. This day she was playing a new game which involved operating a power plant. Nanami's job is to control the generators in the plant and produce maximum output.
There are n generators in the plant. Each generator should be set to a generating level. Generating level is an integer (possibly zero or negative), the generating level of the i-th generator should be between li and ri (both inclusive). The output of a generator can be calculated using a certain quadratic function f(x), where x is the generating level of the generator. Each generator has its own function, the function of the i-th generator is denoted as fi(x).
However, there are m further restrictions to the generators. Let the generating level of the i-th generator be xi. Each restriction is of the form xu \le xv+d, where u and v are IDs of two different generators and d is an integer.
Nanami found the game tedious but giving up is against her creed. So she decided to have a program written to calculate the answer for her (the maximum total output of generators). Somehow, this became your job.
The first line contains two integers n and m(1 \le n \le 50;0 \le m \le 100) - the number of generators and the number of restrictions.
Then follow n lines, each line contains three integers ai, bi, and ci(|ai| \le 10;|bi|,|ci| \le 1000) - the coefficients of the function fi(x). That is, fi(x)=aix2+bix+ci.
Then follow another n lines, each line contains two integers li and ri(-100 \le li \le ri \le 100).
Then follow m lines, each line contains three integers ui, vi, and di(1 \le ui,vi \le n;ui \neq vi;|di| \le 200), describing a restriction. The i-th restriction is xui \le xvi+di.
Print a single line containing a single integer - the maximum output of all the generators. It is guaranteed that there exists at least one valid configuration.
3 3 0 1 0 0 1 1 0 1 2 0 3 1 2 -100 100 1 2 0 2 3 0 3 1 0· \n · · \n · · \n · · \n · \n · \n · \n · · \n · · \n · · \n
9\n
5 8 1 -8 20 2 -4 0 -1 10 -10 0 1 0 0 -1 1 1 9 1 4 0 10 3 11 7 9 2 1 3 1 2 3 2 3 3 3 2 3 3 4 3 4 3 3 4 5 3 5 4 3· \n · · \n · · \n · · \n · · \n · · \n · \n · \n · \n · \n · \n · · \n · · \n · · \n · · \n · · \n · · \n · · \n · · \n
46\n
In the first sample, f1(x)=x, f2(x)=x+1, and f3(x)=x+2, so we are to maximize the sum of the generating levels. The restrictions are x1 \le x2, x2 \le x3, and x3 \le x1, which gives us x1=x2=x3. The optimal configuration is x1=x2=x3=2, which produces an output of 9.
In the second sample, restrictions are equal to |xi-xi+1| \le 3 for 1 \le i \lt n. One of the optimal configurations is x1=1, x2=4, x3=5, x4=8 and x5=7.