[USACO19DEC] Greedy Pie Eaters P

Farmer John has $M$ cows, conveniently labeled $1 \ldots M$, who enjoy the occasional change of pace from eating grass. As a treat for the cows, Farmer John has baked $N$ pies ($1 \leq N \leq 300$), labeled $1 \ldots N$. Cow $i$ enjoys pies with labels in the range $[l_i, r_i]$ (from $l_i$ to $r_i$ inclusive), and no two cows enjoy the exact same range of pies. Cow $i$ also has a weight, $w_i$, which is an integer in the range $1 \ldots 10^6$. Farmer John may choose a sequence of cows $c_1,c_2,\ldots, c_K,$ after which the selected cows will take turns eating in that order. Unfortunately, the cows don't know how to share! When it is cow $c_i$'s turn to eat, she will consume all of the pies that she enjoys --- that is, all remaining pies in the interval $[l_{c_i},r_{c_i}]$. Farmer John would like to avoid the awkward situation occurring when it is a cows turn to eat but all of the pies she enjoys have already been consumed. Therefore, he wants you to compute the largest possible total weight ($w_{c_1}+w_{c_2}+\ldots+w_{c_K}$) of a sequence $c_1,c_2,\ldots, c_K$ for which each cow in the sequence eats at least one pie.

Farmer John 有 $M$ 头奶牛，为了方便，编号为 $1,\dots,M$。这些奶牛平时都吃青草，但是喜欢偶尔换换口味。Farmer John 一天烤了 $N$ 个派请奶牛吃，这 $N$ 个派编号为 $1,\dots,N$。第 $i$ 头奶牛喜欢吃编号在 $\left[ l_i,r_i \right]$ 中的派（包括两端），并且没有两头奶牛喜欢吃相同范围的派。第 $i$ 头奶牛有一个体重 $w_i$，这是一个在 $\left[ 1,10^6 \right]$ 中的正整数。 Farmer John 可以选择一个奶牛序列 $c_1,c_2,\dots,c_K$，并让这些奶牛按这个顺序轮流吃派。不幸的是，这些奶牛不知道分享！当奶牛 吃派时，她会把她喜欢吃的派都吃掉——也就是说，她会吃掉编号在 $[l_{c_i},r_{c_i}]$ 中所有剩余的派。Farmer John 想要避免当轮到一头奶牛吃派时，她所有喜欢的派在之前都被吃掉了这样尴尬的情况。因此，他想让你计算，要使奶牛按 $c_1,c_2,\dots,c_K$ 的顺序吃派，轮到这头奶牛时她喜欢的派至少剩余一个的情况下，这些奶牛的最大可能体重（$w_{c_1}+w_{c_2}+\ldots+w_{c_K}$）是多少。

第一行包含两个正整数 $N,M$； 接下来 $M$ 行，每行三个正整数 $w_i,l_i,r_i$。

输出对于一个合法的序列，最大可能的体重值。

2 2
100 1 2
100 1 1

200

#### 样例解释 在这个样例中，如果奶牛 $1$ 先吃，那么奶牛 $2$ 就吃不到派了。然而，先让奶牛 $2$ 吃，然后奶牛 $1$ 只吃编号为 $2$ 的派，仍可以满足条件。 对于全部数据，$1 \le N \le 300,1 \le M \le \dfrac{N(N-1)}{2},1 \le l_i,r_i \le N,1 \le w_i \le 10^6$。 #### 数据范围 对于测试点 $2-5$，满足 $N \le 50,M \le 20$； 对于测试点 $6-9$，满足 $N \le 50$。 USACO 2019 December 铂金组T1