7296: AtCoder Educational DP Contest —— X - Tower
[Creator : ]
Description
There are N blocks, numbered 1,2,…,N. For each i (1≤i≤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:
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 $s_i$.
Input
Input is given from Standard Input in the following format:
$N$
$w_1\ s_1\ v_1$
$w_2\ s_2\ v_2$
$:$
$w_N\ s_N\ v_N$
$N$
$w_1\ s_1\ v_1$
$w_2\ s_2\ v_2$
$:$
$w_N\ s_N\ v_N$
Output
Print the maximum possible sum of the values of the blocks contained in the tower.
Constraints
All values in input are integers.
$1 \leq N \leq 10^3$
$1 \leq w_i, s_i \leq 10^4$
$1 \leq v_i \leq 10^9$
$1 \leq N \leq 10^3$
$1 \leq w_i, s_i \leq 10^4$
$1 \leq v_i \leq 10^9$
Sample 1 Input
3
2 2 20
2 1 30
3 1 40
Sample 1 Output
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.
Sample 2 Input
4
1 2 10
3 1 10
2 4 10
1 6 10
Sample 2 Output
40
Blocks 1, 2, 3, 4 should be stacked in this order from top to bottom.
Sample 3 Input
5
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
Sample 3 Output
5000000000
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.