#include <bits/stdc++.h>

using namespace std;

int n;
struct Block{
    int w, s, v;

    bool operator < (Block o) const {
        return s + w < o.s + o.w;
    }
};

long long dp[20010];
const long long INF = 1e18;
vector<Block> p;

int main(){
    scanf("%d", &n);

    p.resize(n);

    for(int i = 0; i < n; i++){
        scanf("%d%d%d", &p[i].w, &p[i].s, &p[i].v);
    }

    sort(p.begin(), p.end());

    for(int i = 1; i <= 20000; i++) dp[i] = -INF;

    for(auto k : p){
        int s, w, v;
        s = k.s, w = k.w, v = k.v;

        for(int i = s; i >= 0; i--) dp[i + w] = max(dp[i + w], dp[i] + v);
    }

    long long ans = 0;
    for(int i = 0; i <= 20000; i++) ans = max(ans, dp[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 <bits/stdc++.h>

using namespace std;

int n;
struct Block{
    int w, s, v;

    bool operator < (Block o) const {
        return s + w < o.s + o.w;
    }
};

long long dp[20010];
const long long INF = 1e18;
vector<Block> p;

int main(){
    scanf("%d", &n);

    p.resize(n);

    for(int i = 0; i < n; i++){
        scanf("%d%d%d", &p[i].w, &p[i].s, &p[i].v);
    }

    sort(p.begin(), p.end());

    for(int i = 1; i <= 20000; i++) dp[i] = -INF;

    for(auto k : p){
        int s, w, v;
        s = k.s, w = k.w, v = k.v;

        for(int i = s; i >= 0; i--) dp[i + w] = max(dp[i + w], dp[i] + v);
    }

    long long ans = 0;
    for(int i = 0; i <= 20000; i++) ans = max(ans, dp[i]);

    printf("%lld\n", ans);
    
    return 0;
}
```