#include <bits/stdc++.h>

#define int long long

using namespace std;

const int maxn = 1010, maxl = 10010;
int dp[maxn][maxl], n;

struct item
{
    int w, s, v;
} a[maxn];

signed main()
{
    ios::sync_with_stdio(false);
    cin >> n;

    for (int i = 0; i < n; i++)
        cin >> a[i].w >> a[i].s >> a[i].v;
    sort(a, a + n, [](item u, item v) { return u.w + u.s > v.w + v.s; });

    for (int i = n - 1; ~i; i--)
        for (int j = 0; j < maxl; j++)
        {
            item u = a[i];
            dp[i][j] = dp[i + 1][j];
            if (j >= u.w)
                dp[i][j] = max(dp[i][j], dp[i + 1][min(j - u.w, u.s)] + u.v);
        }

    int ans = 0;
    for (int i = 0; i < n; i++)
        ans = max(ans, dp[i + 1][a[i].s] + a[i].v);

    cout << ans;

    return 0;
}

### Prompt

In CPP, your task is to solve 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>

#define int long long

using namespace std;

const int maxn = 1010, maxl = 10010;
int dp[maxn][maxl], n;

struct item
{
    int w, s, v;
} a[maxn];

signed main()
{
    ios::sync_with_stdio(false);
    cin >> n;

    for (int i = 0; i < n; i++)
        cin >> a[i].w >> a[i].s >> a[i].v;
    sort(a, a + n, [](item u, item v) { return u.w + u.s > v.w + v.s; });

    for (int i = n - 1; ~i; i--)
        for (int j = 0; j < maxl; j++)
        {
            item u = a[i];
            dp[i][j] = dp[i + 1][j];
            if (j >= u.w)
                dp[i][j] = max(dp[i][j], dp[i + 1][min(j - u.w, u.s)] + u.v);
        }

    int ans = 0;
    for (int i = 0; i < n; i++)
        ans = max(ans, dp[i + 1][a[i].s] + a[i].v);

    cout << ans;

    return 0;
}

```