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.

Examples

Input

3
2 2 20
2 1 30
3 1 40

Output

50

Input

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

Output

40

Input

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

Output

5000000000

Input

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

Output

22

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