3257 -- Cow Roller Coaster

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Cow Roller Coaster

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 3352		Accepted: 1401

Description

The cows are building a roller coaster! They want your help to design as fun a roller coaster as possible, while keeping to the budget.

The roller coaster will be built on a long linear stretch of land of length L (1 ≤ L ≤ 1,000). The roller coaster comprises a collection of some of the N (1 ≤ N ≤ 10,000) different interchangable components. Each component i has a fixed length W_i (1 ≤ W_i ≤ L). Due to varying terrain, each component i can be only built starting at location X_i (0 ≤ X_i ≤ L - W_i). The cows want to string together various roller coaster components starting at 0 and ending at L so that the end of each component (except the last) is the start of the next component.

Each component i has a "fun rating" F_i (1 ≤ F_i ≤ 1,000,000) and a cost C_i (1 ≤ C_i ≤ 1000). The total fun of the roller coster is the sum of the fun from each component used; the total cost is likewise the sum of the costs of each component used. The cows' total budget is B (1 ≤ B ≤ 1000). Help the cows determine the most fun roller coaster that they can build with their budget.

Input

Line 1: Three space-separated integers: L, N and B.
Lines 2..N+1: Line i+1 contains four space-separated integers, respectively: X_i, W_i, F_i, and C_i.

Output

Line 1: A single integer that is the maximum fun value that a roller-coaster can have while staying within the budget and meeting all the other constraints. If it is not possible to build a roller-coaster within budget, output -1.

Sample Input

Sample Output

Hint

Taking the 3rd, 5th and 6th components gives a connected roller-coaster with fun value 17 and cost 7. Taking the first two components would give a more fun roller-coaster (25) but would be over budget.

Source

USACO 2006 December Silver