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.
输入描述:
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 ai, bi, and ci (ai ≤ 10; bi, ci ≤ 1000) — the coefficients of the function fi(x). That is, fi(x) = aix2 + bix + ci.Then follow another n lines, each line contains two integers li and ri ( - 100 ≤ li ≤ ri ≤ 100).Then follow m lines, each line contains three integers ui, vi, and di (1 ≤ ui, vi ≤ n; ui ≠ vi; di ≤ 200), describing a restriction. The i-th restriction is xui ≤ xvi + di.
输出描述:
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.
示例1
输入
3 3<br />0 1 0<br />0 1 1<br />0 1 2<br />0 3<br />1 2<br />-100 100<br />1 2 0<br />2 3 0<br />3 1 0<br />5 8<br />1 -8 20<br />2 -4 0<br />-1 10 -10<br />0 1 0<br />0 -1 1<br />1 9<br />1 4<br />0 10<br />3 11<br />7 9<br />2 1 3<br />1 2 3<br />2 3 3<br />3 2 3<br />3 4 3<br />4 3 3<br />4 5 3<br />5 4 3<br />
备注:
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 xi - xi + 1 ≤ 3 for 1 ≤ i n. One of the optimal configurations is x1 = 1, x2 = 4, x3 = 5, x4 = 8 and x5 = 7.
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