
Score : 100 points
Problem StatementThere are N blocks, numbered 1, 2, \ldots, N.
For each i (1 \leq i \leq N), Block i has a weight of w_i, a solidness of s_i and a value of v_i.
Taro has decided to build a tower by choosing some of the N blocks and stacking them vertically in some order.
Here, the tower must satisfy the following condition:
For each Block i contained in the tower, the sum of the weights of the blocks stacked above it is not greater than s_i.
Find the maximum possible sum of the values of the blocks contained in the tower.
Constraints
All values in input are integers.
1 \leq N \leq 10^3
1 \leq w_i, s_i \leq 10^4
1 \leq v_i \leq 10^9
InputInput is given from Standard Input in the following format:
N
w_1 s_1 v_1
w_2 s_2 v_2
:
w_N s_N v_N
OutputPrint the maximum possible sum of the values of the blocks contained in the tower.
Sample Input 13
2 2 20
2 1 30
3 1 40
Sample Output 150
If Blocks 2, 1 are stacked in this order from top to bottom, this tower will satisfy the condition, with the total value of 30 + 20 = 50.
Sample Input 24
1 2 10
3 1 10
2 4 10
1 6 10
Sample Output 240
Blocks 1, 2, 3, 4 should be stacked in this order from top to bottom.
Sample Input 35
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
Sample Output 35000000000
The answer may not fit into a 32-bit integer type.
Sample Input 48
9 5 7
6 2 7
5 7 3
7 8 8
1 9 6
3 3 3
4 1 7
4 5 5
Sample Output 422
We should, for example, stack Blocks 5, 6, 8, 4 in this order from top to bottom.
