HDU 3038 How Many Answers Are Wrong

题目描述

TT and FF are ... friends. Uh... very very good friends -________-b

FF is a bad boy, he is always wooing TT to play the following game with him. This is a very humdrum game. To begin with, TT should write down a sequence of integers-_-!!(bored).

Then, FF can choose a continuous subsequence from it(for example the subsequence from the third to the fifth integer inclusively). After that, FF will ask TT what the sum of the subsequence he chose is. The next, TT will answer FF's question. Then, FF can redo this process. In the end, FF must work out the entire sequence of integers.

Boring~~ Boring~~ a very very boring game!!! TT doesn't want to play with FF at all. To punish FF, she often tells FF the wrong answers on purpose.

The bad boy is not a fool man. FF detects some answers are incompatible. Of course, these contradictions make it difficult to calculate the sequence.

However, TT is a nice and lovely girl. She doesn't have the heart to be hard on FF. To save time, she guarantees that the answers are all right if there is no logical mistakes indeed.

What's more, if FF finds an answer to be wrong, he will ignore it when judging next answers.

But there will be so many questions that poor FF can't make sure whether the current answer is right or wrong in a moment. So he decides to write a program to help him with this matter. The program will receive a series of questions from FF together with the answers FF has received from TT. The aim of this program is to find how many answers are wrong. Only by ignoring the wrong answers can FF work out the entire sequence of integers. Poor FF has no time to do this job. And now he is asking for your help~(Why asking trouble for himself~~Bad boy)

TT 和 FF 是……朋友。呃……非常非常要好的朋友 -________-b

FF 是个坏男孩，他总是缠着 TT 和他玩下面这个游戏。这是一个非常单调的游戏。一开始，TT 应该写下一系列整数 -_-

然后，FF 可以从中选择一个连续的子序列（例如从第三个到第五个整数，包括这两个）。之后，FF 会问 TT 这个子序列的和是多少。接下来，TT 会回答 FF 的问题。然后，FF 可以重新开始这个过程。最后，FF 必须推断出整个整数序列。

无聊啊~~ 无聊~~一个非常非常无聊的游戏!!! TT 根本不想和 FF 玩这个游戏。为了惩罚 FF，她经常故意给出错误的答案。

坏男孩可不是傻子。FF 发现有些答案是不一致的。当然，这些矛盾让推断序列变得困难。

不过，TT 是个善良可爱的女孩。她不忍心对 FF 太苛刻。为了节省时间，她保证如果逻辑上没有错误，答案都是正确的。

此外，如果 FF 发现某个答案是错的，他会忽略它，以便判断后续的答案。

但问题是有太多问题了，可怜的 FF 无法立刻判断当前答案是否正确。所以他决定写一个程序来帮助他。这个程序会接收一系列 FF 的问题以及 TT 的回答。这个程序的目标是找出有多少个答案是错的。只有忽略错误的答案，FF 才能推断出整个整数序列。可怜的 FF 没有时间做这个工作。现在他向你寻求帮助~（自找麻烦的坏男孩）

输入格式

有多组测试

Line 1: Two integers, N and M ($1 <= N <= 200000, 1 <= M <= 40000$). Means TT wrote N integers and FF asked her M questions.

Line 2..M+1: Line i+1 contains three integer: Ai, Bi and Si. Means TT answered FF that the sum from Ai to Bi is Si. It's guaranteed that $0 < A_i <= B_i <= N$.

You can assume that any sum of subsequence is fit in 32-bit integer.

输出格式

A single line with a integer denotes how many answers are wrong.

样例

10 5
1 10 100
7 10 28
1 3 32
4 6 41
6 6 1

1

SOURCE

HDU 3038