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D. Nanami's Power Plant

time limit per test

5 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputNanami 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*_{ui} ≤ *x*_{vi} + *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.

Examples

Input

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

Output

9

Input

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

Output

46

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.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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