#include <iostream>
#include <algorithm>

using namespace std;

struct block {
    int w, s, v;
    bool operator<(block a) const {
        return w + s < a.w + a.s;
    }
};

long long dp[20001]; // dp[i] is max value with weight of i

int main() {
    ios_base::sync_with_stdio(false); cin.tie(0);
    int n; cin >> n;
    block blocks[n];
    for (int i = 0; i < n; i++) cin >> blocks[i].w >> blocks[i].s >> blocks[i].v;
    sort(blocks, blocks + n);
    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);
    }
    long long ans = 0;
    for (int i = 0; i < 20001; i++) ans = max(ans, dp[i]);
    cout << ans;
    return 0;
}

### Prompt

Please create a solution in cpp 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 <iostream>
#include <algorithm>

using namespace std;

struct block {
    int w, s, v;
    bool operator<(block a) const {
        return w + s < a.w + a.s;
    }
};

long long dp[20001]; // dp[i] is max value with weight of i

int main() {
    ios_base::sync_with_stdio(false); cin.tie(0);
    int n; cin >> n;
    block blocks[n];
    for (int i = 0; i < n; i++) cin >> blocks[i].w >> blocks[i].s >> blocks[i].v;
    sort(blocks, blocks + n);
    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);
    }
    long long ans = 0;
    for (int i = 0; i < 20001; i++) ans = max(ans, dp[i]);
    cout << ans;
    return 0;
}

```