## Best Hat in Town II

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Points: 25
Time limit: 2.0s
Memory limit: 256M

Authors:
Problem types

The Mad Hatter's hat-searching quest now continues in a new town. In this town, there are varieties of hats (numbered from to ) being traded at stores (numbered from to ). The -th store will sell a hat of type in exchange for any hat whose type is between and (inclusive). The Mad Hatter can perform a trade at the same store more than once.

The Mad Hatter starts with a single hat of type . What is the maximum possible number of distinct hat types that he can wear at least once?

.

#### Input Format

The first line contains two space-separated integers and .

lines follow; the -th one contains three space-separated integers , , and .

#### Output Format

Output a single integer: the maximum number of hat types that can be worn.

#### Sample Input 1

5 4
4 1 2
5 1 1
2 4 4
3 4 5

#### Output for Sample Input 1

4

#### Explanation for Sample Input 1

It is possible to wear hats of type 1,2,3, and 4 using the sequence of trades .

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