#include <bits/stdc++.h>
using namespace std;
#define int long long
#define ii pair<int, int>
#define vi vector<int>
#define pb emplace_back
#define sz(x) (int)x.size()
#define all(v) v.begin(), v.end()
#define x first
#define y second
#define rep(i, j, k) for(i=j; i<k; i++)
#define sep(i, j, k) for(i=j; i>k; i--)
const int N = 2e4+5, inf = 1e9+7;
int n, k, i, j;
struct nd{int w, s, v;};
nd v[N];
int dp[N];
bool cmp(nd&a, nd&b){ return a.w+a.s<b.w+b.s; }
signed main()
{
    ios_base::sync_with_stdio(false); cin.tie(0);
    int i, j, a, b, ans = 0;
    cin>>n;
    rep(i, 1, n+1) cin>>v[i].w>>v[i].s>>v[i].v;
    sort(v+1, v+n+1, cmp);
    rep(i, 1, n+1)
        for(int w = v[i].s; w >= 0; w--)
            dp[w+v[i].w] = max(dp[w+v[i].w], dp[w]+v[i].v);
    cout<<*max_element(dp, dp+N);
}
### Prompt

Create a solution in CPP for 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 int long long
#define ii pair<int, int>
#define vi vector<int>
#define pb emplace_back
#define sz(x) (int)x.size()
#define all(v) v.begin(), v.end()
#define x first
#define y second
#define rep(i, j, k) for(i=j; i<k; i++)
#define sep(i, j, k) for(i=j; i>k; i--)
const int N = 2e4+5, inf = 1e9+7;
int n, k, i, j;
struct nd{int w, s, v;};
nd v[N];
int dp[N];
bool cmp(nd&a, nd&b){ return a.w+a.s<b.w+b.s; }
signed main()
{
    ios_base::sync_with_stdio(false); cin.tie(0);
    int i, j, a, b, ans = 0;
    cin>>n;
    rep(i, 1, n+1) cin>>v[i].w>>v[i].s>>v[i].v;
    sort(v+1, v+n+1, cmp);
    rep(i, 1, n+1)
        for(int w = v[i].s; w >= 0; w--)
            dp[w+v[i].w] = max(dp[w+v[i].w], dp[w]+v[i].v);
    cout<<*max_element(dp, dp+N);
}
```