Berland local ICPC challenge has quite recently finished. There were m members numbered from 1 to m, who contended on a problemset of n issues numbered from 1 to n.    Presently the article is going to happen. There are two issue creators, every one of them will tell the instructional exercise to precisely k back to back

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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Berland local ICPC challenge has quite recently finished. There were m members numbered from 1 to m, who contended on a problemset of n issues numbered from 1 to n. 

 

Presently the article is going to happen. There are two issue creators, every one of them will tell the instructional exercise to precisely k back to back errands of the problemset. The creators pick the section of k continuous errands for themselves autonomously of one another. The sections can correspond, meet or not cross by any means. 

 

The I-th member is keen on paying attention to the instructional exercise of all continuous errands from li to ri. Every member consistently decides to pay attention to just the issue creator that tells the instructional exercises to the most extreme number of assignments he is keen on. Leave this greatest number alone artificial intelligence. No member can pay attention to both of the creators, regardless of whether their sections converge. 

 

The creators need to pick the portions of k sequential undertakings for themselves so that the amount of computer based intelligence over all members is amplified. 

 

Input 

 

The primary line contains three integers n,m and k (1≤n,m≤2000, 1≤k≤n) — the number of issues, the number of members and the length of the portion of errands every one of the issue creators intends to tell the instructional exercise to. 

 

The I-th of the following m lines contains two integers li and ri (1≤li≤ri≤n) — the portion of assignments the I-th member is keen on paying attention to the instructional exercise to. 

 

Output 

 

Print a solitary integer — the most extreme amount of computer based intelligence over all members

 

 

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