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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* _{ 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.

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 2010-2020 Mike Mirzayanov

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