D. Nanami's Power Plant
time limit per test
5 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

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 ≤ nu 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.