#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
#include <queue>
#include <vector>
#include <map>
#include <set>
#define MAXN 1005
#define MAXM 10005
#define INF 0x3f3f3f3f
#define rint register int
#define LL long long
#define LD long double
using namespace std;

int n;
LL ans, f[MAXM*2];

struct A {int w, s, v;} a[MAXN];

bool CMP(A x, A y)
{
    return x.w+x.s<y.w+y.s;
}

int main()
{
    scanf("%d", &n);
    for(rint 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(rint i=1; i<=n; ++i)
	for(rint j=a[i].s; j>=0; j--) f[j+a[i].w]=max(f[j+a[i].w], f[j]+a[i].v);
    for(rint i=0; i<=20000; ++i) ans=max(ans, f[i]);
    printf("%lld\n", ans);
    return 0;
}

### Prompt

Construct a cpp code solution to the problem outlined:

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 <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
#include <queue>
#include <vector>
#include <map>
#include <set>
#define MAXN 1005
#define MAXM 10005
#define INF 0x3f3f3f3f
#define rint register int
#define LL long long
#define LD long double
using namespace std;

int n;
LL ans, f[MAXM*2];

struct A {int w, s, v;} a[MAXN];

bool CMP(A x, A y)
{
    return x.w+x.s<y.w+y.s;
}

int main()
{
    scanf("%d", &n);
    for(rint 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(rint i=1; i<=n; ++i)
	for(rint j=a[i].s; j>=0; j--) f[j+a[i].w]=max(f[j+a[i].w], f[j]+a[i].v);
    for(rint i=0; i<=20000; ++i) ans=max(ans, f[i]);
    printf("%lld\n", ans);
    return 0;
}

```