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 (3.4.3) (judge verdict: Time Limit Exceeded)

N=int(input())
TT=[]
for _ in range(N):
    w,s,v=list(map(int,input().strip().split(' ')))
    TT+=[(w,s,v)]
TT=sorted(TT,key=lambda X:X[1]+X[0])
dp=[[0]*(10**4+1) for i in range(N)]

#for L in range()
#dp[i][weight]=max(dp[i-1][weight-W[i]]+V[i],dp[i-1][weight]
for i in range(N):
    if i==0:
        dp[0][TT[0][0]]=TT[0][2]
        continue
    
    
    for weight in range(1,10**4+1):
        if TT[i][1]>=weight-TT[i][0] and weight-TT[i][0]>=0:
            dp[i][weight]=max(dp[i-1][weight],dp[i-1][weight-TT[i][0]]+TT[i][2])
        else:
            dp[i][weight]=dp[i-1][weight]
print(max(dp[-1]))