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Problem 1545 Milking Time

Problem Description

Bessie is such a hard-working cow. In fact, she is so focused on maximizing her productivity that she decides to schedule her next N (1<=N<=1,000,000) hours (conveniently labeled 0..N-1) so that she produces as much milk as possible.

Farmer John has a list of M (1<=M<=1,000) possibly overlapping intervals in which he is available for milking. Each interval i has a starting hour (0<=starting_hour_i<N), an ending hour (starting_hour_i<ending_hour_i<=N), and a corresponding efficiency (1<=efficiency_i<=1,000,000) which indicates how many gallons of milk that he can get out of Bessie in that interval. Farmer John starts and stops milking at the beginning of the starting hour and ending hour, respectively. When being milked, Bessie must be milked through an entire interval.

Even Bessie has her limitations, though. After being milked during any interval, she must rest R (1<=R<=N) hours before she can start milking again. Given Farmer Johns list of intervals, determine the maximum amount of milk that Bessie can produce in the N hours.

Input

The input will consist of several datasets.
Each dataset contains tree parts:
*Line 1:Three space-separated integers: N, M, and R.
*Lines 2..M+1:Line i+1 describes FJ's ith milking interval with three space-separated integers: tarting_hour_i, ending_hour_i, and efficiency_i
Input is terminated by end of file.

Output

For each dataset,you should output the maximum number of gallons of milk that Bessie can product in the N hours in one line.

Sample Input

12 4 2 1 2 8 10 12 19 3 6 24 7 10 31

43

Hint

Output Details:
Bessie wants to schedule the next 12 hours; Farmer John has four intervals in which he can milk her; Bessie must rest 2 hours after every milking. The first interval lasts from hour 1 to hour 2, the second from hour 10 to hour 12, the third from hour 3 to hour 6, and the fourth from hour 7 to hour 10. Farmer John can get 8, 19, 24, and 31 gallons of milk, respectively, from Bessie in those intervals.
Output Details:
If Bessie uses the first interval, she cannot use the third because she needs 2 hours of rest. If she uses the second, she cannot use the fourth. Lastly, if she uses the third, she cannot use the fourth. The best situation is choosing the second and third intervals, producing 43 gallons of milk.

Source

USACO 2007 November

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