Problem:
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.

Sample Input 1

3
2 2 20
2 1 30
3 1 40

Sample Output 1

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 Input 2

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

Sample Output 2

40

Blocks 1, 2, 3, 4 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

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

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

Solution in Python (3.8.2) (judge verdict: Time Limit Exceeded)

n = int(input())
blocks = []
for i in range(n):
    w_str, s_str, v_str = input().split(" ")
    w, s, v = int(w_str), int(s_str), int(v_str)
    blocks.append({"w": w, "s": s, "v": v})

blocks = sorted(blocks, key=lambda block: block["s"]) 

def dp(blocks, max_s):
    max_val = 0
    for i in range(len(blocks)):
        taken =  blocks[i]

        # klo constraint nya
        new_max_s = 0
        if max_s is None:
            new_max_s = taken["s"]
        else:
            new_max_s = min(max_s-taken["w"], taken["s"])

        # ini constraint nya
        if new_max_s < 0:
            continue

        # remaining blocks, taruh sini, biar ga diitung kalau jelas ga mungkin
        remaining_blocks = [blocks[x] for x in range(len(blocks)) if x != i]

        # ini nilai tambahan
        taken_val = taken["v"]
        new_val = taken_val + dp(remaining_blocks, new_max_s)
        if new_val > max_val:
            max_val = new_val

    return max_val

print(dp(blocks, None))