Score : $100$ points

Problem Statement

There 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.
• $1 \leq N \leq 10^3$
• $1 \leq w_i, s_i \leq 10^4$
• $1 \leq v_i \leq 10^9$

Input

Input is given from Standard Input in the following format:

$N$

$w_1$ $s_1$ $v_1$

$w_2$ $s_2$ $v_2$

$:$

$w_N$ $s_N$ $v_N$

Output

Print the maximum possible sum of the values of the blocks contained in the tower.

3
2 2 20
2 1 30
3 1 40

50

If Blocks $2, 1$ are stacked in this order from top to bottom, this tower will satisfy the condition, with the total value of $30 + 20 = 50$.

4
1 2 10
3 1 10
2 4 10
1 6 10

40

Blocks $1, 2, 3, 4$ should be stacked in this order from top to bottom.

5
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000

5000000000

The answer may not fit into a 32-bit integer type.

8
9 5 7
6 2 7
5 7 3
7 8 8
1 9 6
3 3 3
4 1 7
4 5 5

22

We should, for example, stack Blocks $5, 6, 8, 4$ in this order from top to bottom.