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_ix² + b_ix + 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, f₁(x) = x, f₂(x) = x + 1, and f₃(x) = x + 2, so we are to maximize the sum of the generating levels. The restrictions are x₁ ≤ x₂, x₂ ≤ x₃, and x₃ ≤ x₁, which gives us x₁ = x₂ = x₃. The optimal configuration is x₁ = x₂ = x₃ = 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 x₁ = 1, x₂ = 4, x₃ = 5, x₄ = 8 and x₅ = 7.

Idx	Name	Rating	Status
D	Nanami's Power Plant	2900
E	Furukawa Nagisa's Tree	3000

Codeforces Round 248 (Div. 1)