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 PyPy3 (2.4.0) (judge verdict: Accepted)

import sys
input = sys.stdin.readline

N=int(input())
B=sorted([list(map(int,input().split())) for i in range(N)],key=lambda x:x[0]+x[1])
#W+Sの順にソートすると無駄がない。

DP=[0]*(10**4+2)
#重さの合計がWのときの価値。
#W=10**4+1ならそれ以上更新されないので、W>=10**4+1以上のものはそこに置く

for w,s,v in B:
    
    if 10**4+1-w<=s:
        x=max(DP[10**4+1-w:s+1])+v
        if DP[-1]<x:
            DP[-1]=x

    if 10**4-w<s:
        for i in range(10**4-w,-1,-1):
            if DP[i+w]<DP[i]+v:
                DP[i+w]=DP[i]+v

    else:
        for i in range(s,-1,-1):
            if DP[i+w]<DP[i]+v:
                DP[i+w]=DP[i]+v        

print(max(DP))