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.

Input

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 $*x*_{*u*_{*i*}} ≤ *x*_{*v*_{*i*}} + *d*_{*i*}$.

Output

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.

Note

In the first sample, $*f*_{1}(*x*) = *x*$, $*f*_{2}(*x*) = *x* + 1$, and $*f*_{3}(*x*) = *x* + 2$, so we are to maximize the sum of the generating levels. The restrictions are $*x*_{1} ≤ *x*_{2}$, $*x*_{2} ≤ *x*_{3}$, and $*x*_{3} ≤ *x*_{1}$, which gives us $*x*_{1} = *x*_{2} = *x*_{3}$. The optimal configuration is $*x*_{1} = *x*_{2} = *x*_{3} = 2$, which produces an output of 9.

In the second sample, restrictions are equal to $|*x*_{*i*} - *x*_{*i* + 1}| ≤ 3$ for $1 ≤ *i* < *n*$. One of the optimal configurations is $*x*_{1} = 1$, $*x*_{2} = 4$, $*x*_{3} = 5$, $*x*_{4} = 8$ and $*x*_{5} = 7$.