## Educational DP Contest AtCoder X - Tower

View as PDF

Points: 20
Time limit: 1.0s
Memory limit: 1G

Problem type

There are blocks, numbered . For each , Block has a weight of , a solidness of , and a value of .

Taro has decided to build a tower by choosing some of the blocks and stacking them vertically in some order. Here, the tower must satisfy the following condition:

• For each Block contained in the tower, the sum of the weights of the blocks stacked above it is not greater than .

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

#### Constraints

• All values in input are integers.

#### Input Specification

The first line will contain the integer .

The next lines will each contain three integers, .

#### Output Specification

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

#### Sample Input 1

3
2 2 20
2 1 30
3 1 40

#### Sample Output 1

50

#### Explanation For Sample 1

If Blocks are stacked in this order from top to bottom, this tower will satisfy the condition, with the total value of .

#### Sample Input 2

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

#### Sample Output 2

40

#### Explanation For Sample 2

Blocks should be stacked in this order from top to bottom.

#### Sample Input 3

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

#### Sample Output 3

5000000000

#### Explanation For Sample 3

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

#### Sample Input 4

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

#### Sample Output 4

22

#### Explanation For Sample 4

We should, for example, stack Blocks in this order from top to bottom.