Space Elevator

Time Limit: 1000MS

Memory Limit: 65536K


The cows are going to space! They plan to achieve orbit by building a sort of space elevator: a giant tower of blocks. They have K (1 <= K <= 400) different types of blocks with which to build the tower. Each block of type i has height h_i (1 <= h_i <= 100) and is available in quantity c_i (1 <= c_i <= 10). Due to possible damage caused by cosmic rays, no part of a block of type i can exceed a maximum altitude a_i (1 <= a_i <= 40000). Help the cows build the tallest space elevator possible by stacking blocks on top of each other according to the rules.


* Line 1: A single integer, K * Lines 2..K+1: Each line contains three space-separated integers: h_i, a_i, and c_i. Line i+1 describes block type i.


* Line 1: A single integer H, the maximum height of a tower that can be built

Sample Input

7 40 3
5 23 8
2 52 6

Sample Output




From the bottom: 3 blocks of type 2, below 3 of type 1, below 6 of type 3. Stacking 4 blocks of type 2 and 3 of type 1 is not legal, since the top of the last type 1 block would exceed height 40.


USACO 2005 March Gold