题目描述

The aliens from outer space have (finally!) invaded Earth. Defend yourself, or be disintegrated!

Or assimilated. Or eaten. We are not yet sure.

The aliens follow a known attack pattern. There are $n$ attackers, the $i-th$ one appears at time $a_i$, at distance $d_i$ from you. He must be destroyed no later than at time $b_i$, or else he will fire his weapon, which will definitely end the fight.

Your weapon is an area-blaster, which can be set to any given power. If fired with power $R$,it momentarily destroys all aliens at distance $R$ or smaller. It also consumes $R$ fuel cells.

Determine the minimal cost (measured in fuel cells) of destroying all the aliens, without being killed.

输入格式

The first line of input contains the number of test cases $T$. The descriptions of the test cases follow:

Each test case starts with a line containing the number of aliens $n(1 \le n \le 300)$. Of the next $n$ lines, the $i-th$ one contains three integers $a_i, b_i, d_i, (1 \le a_i < b_i \le 10 000, 1 \le d_i \le 10 000)$.

The $i-th$ alien appears at time $a_i$, is idle until $b_i$, and his distance from you is $d_i$.

输出格式

For each test case, output one line containing the minimum number of cells needed to destroy all the aliens.

题目大意

题目描述

来自外太空的外星人（最终）入侵了地球。保卫自己，或者解体，被他们同化，或者成为食物。迄今为止，我们无法确定。

外星人遵循已知的攻击模式。有 $N$ 个外星人进攻，第 $i$ 个进攻的外星人会在时间 $a_i$ 出现，距离你的距离为 $d_i$，它必须在时间 $b_i$ 前被消灭，否则被消灭的会是你。

你的武器是一个区域冲击波器，可以设置任何给定的功率。如果被设置了功率 $R$，它会瞬间摧毁与你的距离在 $R$ 以内的所有外星人（可以等于），同时它也会消耗 $R$ 单位的燃料电池。

求摧毁所有外星人的最低成本（消耗多少燃料电池），同时保证自己的生命安全。

输入格式

第一行输入一个数 $T$,表示有 $T$ 组数据。

每组数据的第一行为外星人的数量 $n$（$1\leq n\leq 300$）。

接下来 $n$ 行，每行有三个数 $a_i,b_i,d_i$，表示这个外星人在时间 $a_i$ 出现，距离你 $d_i$，在 $b_i$ 前时刻死亡。

输出格式

共 $T$ 行，每行输出摧毁所有外星人的最低成本。

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