#include <iostream>
#include <algorithm>
#include <vector>

using namespace std;
typedef long long ll;
#define REP(i,n) for (int i = 0; i < n; ++i)
#define ALL(x) x.begin(), x.end()

const int MAX = 2e4+10;
struct block {
    int w, s, v;

    bool operator<( const block& right ) const {
        return s+w > right.s+right.w;
    }
};
vector<block> B;
ll dp[MAX];

int N;

int main () {
	cin >> N;
    B = vector<block>(N);
    REP (i, N) cin >> B[i].w >> B[i].s >> B[i].v;
    sort(ALL(B));

    ll ans = 0;
    REP (i, N) {
        REP (j, B[i].s+1)
            dp[j] = max(dp[j], dp[j+B[i].w]+B[i].v);
    }
    REP (i, MAX) ans = max(ans, dp[i]);
    cout << ans << endl;
}
### 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 <iostream>
#include <algorithm>
#include <vector>

using namespace std;
typedef long long ll;
#define REP(i,n) for (int i = 0; i < n; ++i)
#define ALL(x) x.begin(), x.end()

const int MAX = 2e4+10;
struct block {
    int w, s, v;

    bool operator<( const block& right ) const {
        return s+w > right.s+right.w;
    }
};
vector<block> B;
ll dp[MAX];

int N;

int main () {
	cin >> N;
    B = vector<block>(N);
    REP (i, N) cin >> B[i].w >> B[i].s >> B[i].v;
    sort(ALL(B));

    ll ans = 0;
    REP (i, N) {
        REP (j, B[i].s+1)
            dp[j] = max(dp[j], dp[j+B[i].w]+B[i].v);
    }
    REP (i, MAX) ans = max(ans, dp[i]);
    cout << ans << endl;
}
```