Minimum Microphones

Brett's class has a performance where each of the $n$ students stands in a row holding a microphone while singing a song. The class is divided into $m$ contiguous groups, where the $i$-th group consists of students with indices from $a_i$ to $b_i$ (inclusive). Note that a student may belong to multiple groups or none at all. To ensure a good performance, each group must have at least $c_i$ students holding microphones. Your task is to determine the minimum number of microphones required.

inputFormat

The first line contains two integers $n$ and $m$. Each of the following $m$ lines contains three integers $a_i$, $b_i$, and $c_i$, representing the starting and ending indices of the $i$-th group and the minimum number of microphones required for that group, respectively.

outputFormat

Output a single integer, the minimum number of microphones needed.

sample

5 2
1 3 2
4 5 1

3