Nanami's Power Plant
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 *l**i* and *r**i* (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 *f**i*(*x*).

However, there are *m* further restrictions to the generators. Let the generating level of the *i*-th generator be *x**i*. Each restriction is of the form *x**u*<=≤<=*x**v*<=+<=*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 *a**i*, *b**i*, and *c**i* (|*a**i*|<=≤<=10; |*b**i*|,<=|*c**i*|<=≤<=1000) — the coefficients of the function *f**i*(*x*). That is, *f**i*(*x*)<==<=*a**i**x*2<=+<=*b**i**x*<=+<=*c**i*.

Then follow another *n* lines, each line contains two integers *l**i* and *r**i* (<=-<=100<=≤<=*l**i*<=≤<=*r**i*<=≤<=100).

Then follow *m* lines, each line contains three integers *u**i*, *v**i*, and *d**i* (1<=≤<=*u**i*,<=*v**i*<=≤<=*n*; *u**i*<=≠<=*v**i*; |*d**i*|<=≤<=200), describing a restriction. The *i*-th restriction is *x**u**i*<=≤<=*x**v**i*<=+<=*d**i*.
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.
In the first sample, *f*<sub class="lower-index">1</sub>(*x*) = *x*, *f*<sub class="lower-index">2</sub>(*x*) = *x* + 1, and *f*<sub class="lower-index">3</sub>(*x*) = *x* + 2, so we are to maximize the sum of the generating levels. The restrictions are *x*<sub class="lower-index">1</sub> ≤ *x*<sub class="lower-index">2</sub>, *x*<sub class="lower-index">2</sub> ≤ *x*<sub class="lower-index">3</sub>, and *x*<sub class="lower-index">3</sub> ≤ *x*<sub class="lower-index">1</sub>, which gives us *x*<sub class="lower-index">1</sub> = *x*<sub class="lower-index">2</sub> = *x*<sub class="lower-index">3</sub>. The optimal configuration is *x*<sub class="lower-index">1</sub> = *x*<sub class="lower-index">2</sub> = *x*<sub class="lower-index">3</sub> = 2, which produces an output of 9.

In the second sample, restrictions are equal to |*x*<sub class="lower-index">*i*</sub> - *x*<sub class="lower-index">*i* + 1</sub>| ≤ 3 for 1 ≤ *i* &lt; *n*. One of the optimal configurations is *x*<sub class="lower-index">1</sub> = 1, *x*<sub class="lower-index">2</sub> = 4, *x*<sub class="lower-index">3</sub> = 5, *x*<sub class="lower-index">4</sub> = 8 and *x*<sub class="lower-index">5</sub> = 7.