#include <bits/stdc++.h>

typedef long long ll;
const int MAX_N = 1000, MAX_W = 2e4;

using namespace std;

const int W = 10000;

struct Block {
    int w;
    int s;
    int v;
};

Block blocks[1 + MAX_N];

bool operator < (Block a, Block b) {
    return a.w + a.s < b.w + b.s;
}

ll mxv[1 + MAX_W + 1];

int main () {
    int n;
    cin >> n;
    for (int i = 1; i <= n; i++)
        cin >> blocks[i].w >> blocks[i].s >> blocks[i].v;
    sort (blocks + 1, blocks + n + 1);
    for (int i = 1; i <= n; i++)
        for (int j = W; j >= 0; j--)
            if (j <= blocks[i].s)
                mxv[j + blocks[i].w] = max (mxv[j + blocks[i].w],  mxv[j] + blocks[i].v);
    ll ans = 0;
    for (int i = 0; i <= W * 2; i++)
        ans = max (ans, mxv[i]);
    cout << ans << "\n";
    return 0;
}

### Prompt

Your challenge is to write a Cpp solution to 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>

typedef long long ll;
const int MAX_N = 1000, MAX_W = 2e4;

using namespace std;

const int W = 10000;

struct Block {
    int w;
    int s;
    int v;
};

Block blocks[1 + MAX_N];

bool operator < (Block a, Block b) {
    return a.w + a.s < b.w + b.s;
}

ll mxv[1 + MAX_W + 1];

int main () {
    int n;
    cin >> n;
    for (int i = 1; i <= n; i++)
        cin >> blocks[i].w >> blocks[i].s >> blocks[i].v;
    sort (blocks + 1, blocks + n + 1);
    for (int i = 1; i <= n; i++)
        for (int j = W; j >= 0; j--)
            if (j <= blocks[i].s)
                mxv[j + blocks[i].w] = max (mxv[j + blocks[i].w],  mxv[j] + blocks[i].v);
    ll ans = 0;
    for (int i = 0; i <= W * 2; i++)
        ans = max (ans, mxv[i]);
    cout << ans << "\n";
    return 0;
}

```