#include <bits/stdc++.h>
using namespace std;
typedef pair<int,int> pii;
typedef long long ll;
const int MN = 1e3+2, MS = 2e4+2;
struct block {
    int w,s,v;
} blocks[MN];
ll dp[MS];
int main() {
    int n; ll ret = 0;
    scanf ("%d",&n);
    for (int i = 0; i < n; i++) scanf ("%d%d%d",&blocks[i].w,&blocks[i].s,&blocks[i].v);
    sort(blocks,blocks+n,[](block a, block b) {return a.w + a.s < b.w + b.s;});
    for (int i = 0; i < n; i++) for (int j = blocks[i].s; j >= 0; j--) dp[j+blocks[i].w] = max(dp[j+blocks[i].w],dp[j]+blocks[i].v);
    for (int i = 0; i < MS; i++ ) ret = max(ret,dp[i]);
    printf ("%lld\n",ret);
    return 0;
}
### Prompt

Develop a solution in CPP to the problem described below:

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;
typedef pair<int,int> pii;
typedef long long ll;
const int MN = 1e3+2, MS = 2e4+2;
struct block {
    int w,s,v;
} blocks[MN];
ll dp[MS];
int main() {
    int n; ll ret = 0;
    scanf ("%d",&n);
    for (int i = 0; i < n; i++) scanf ("%d%d%d",&blocks[i].w,&blocks[i].s,&blocks[i].v);
    sort(blocks,blocks+n,[](block a, block b) {return a.w + a.s < b.w + b.s;});
    for (int i = 0; i < n; i++) for (int j = blocks[i].s; j >= 0; j--) dp[j+blocks[i].w] = max(dp[j+blocks[i].w],dp[j]+blocks[i].v);
    for (int i = 0; i < MS; i++ ) ret = max(ret,dp[i]);
    printf ("%lld\n",ret);
    return 0;
}
```