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≤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≤n≤50;0≤m≤100) − the number of generators and the number of restrictions.
Then follow n lines, each line contains three integers ai, bi, and ci(|ai|≤10;|bi|,|ci|≤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≤li≤ri≤100).
Then follow m lines, each line contains three integers ui, vi, and di(1≤ui,vi≤n;ui≠vi;|di|≤200), describing a restriction. The i-th restriction is xui≤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
9
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
46
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≤x2, x2≤x3, and x3≤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|≤3 for 1≤i<n. One of the optimal configurations is x1=1, x2=4, x3=5, x4=8 and x5=7.