#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define M 20001
#define N 1001
struct faner {
    int w, s, v;
} a[N];
ll f[M], ans;
bool cmp(faner a, faner b) { return a.s + a.w < b.s + b.w; }
int n;
int main() {
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) scanf("%d%d%d", &a[i].w, &a[i].s, &a[i].v);
    sort(a + 1, a + n + 1, cmp);
    for (int i = 1; i <= n; i++)
        for (int j = M - 1; j >= a[i].w; j--)
            if (a[i].s + a[i].w >= j) f[j] = max(f[j], f[j - a[i].w] + a[i].v);
    for (int i = 1; i < M; i++) ans = max(ans, f[i]);
    printf("%lld\n", ans);
    return 0;
}
### Prompt

Your task is to create a CPP solution to the following problem:

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define M 20001
#define N 1001
struct faner {
    int w, s, v;
} a[N];
ll f[M], ans;
bool cmp(faner a, faner b) { return a.s + a.w < b.s + b.w; }
int n;
int main() {
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) scanf("%d%d%d", &a[i].w, &a[i].s, &a[i].v);
    sort(a + 1, a + n + 1, cmp);
    for (int i = 1; i <= n; i++)
        for (int j = M - 1; j >= a[i].w; j--)
            if (a[i].s + a[i].w >= j) f[j] = max(f[j], f[j - a[i].w] + a[i].v);
    for (int i = 1; i < M; i++) ans = max(ans, f[i]);
    printf("%lld\n", ans);
    return 0;
}
```