p03183 Educational DP Contest - 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
```python
import sys
input = lambda : sys.stdin.readline().strip()

n = int(input())
wsv = [list(map(int, input().split())) for i in range(n)]
wsv.sort(key=lambda x: x[0]+x[1])

max_s = 10**4
DP = [-float("inf")]*(2*max_s+1)

DP[0] = 0

for i in range(n):
    w,s,v = wsv[i]
    nxt = DP[:]
    for j in range(s+1):
        nxt[j+w] = max(DP[j]+v, nxt[j+w])
    DP = nxt

ans = max(DP)
print(ans)
```