Tower

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

inputFormat

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

outputFormat

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

样例

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

5000000000