#include<bits/stdc++.h>
using namespace std;

#define all(x) begin(x), end(x)

using i64 = int_fast64_t;
using u64 = uint_fast64_t;
using f64 = double;
using p64 = pair<i64, i64>;

constexpr i64 INF = INT_FAST64_MAX / 2;

struct block { i64 w, s, v; };

void solve() {
    i64 n;
    cin >> n;

    vector<block> b(n);
    for (auto& [ w, s, v ] : b) cin >> w >> s >> v;
    sort(all(b), [](block &x, block &y) { return x.w + x.s < y.w + y.s; });

    vector<i64> dp(2e4 + 10);
    for (auto& [ w, s, v ] : b) {
        for (i64 i = s; i >= 0; i--) {
            dp[i + w] = max(dp[i + w], dp[i] + v);
        }
    }
    cout << *max_element(all(dp)) << endl;
}

int main() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    solve();
}

### 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<bits/stdc++.h>
using namespace std;

#define all(x) begin(x), end(x)

using i64 = int_fast64_t;
using u64 = uint_fast64_t;
using f64 = double;
using p64 = pair<i64, i64>;

constexpr i64 INF = INT_FAST64_MAX / 2;

struct block { i64 w, s, v; };

void solve() {
    i64 n;
    cin >> n;

    vector<block> b(n);
    for (auto& [ w, s, v ] : b) cin >> w >> s >> v;
    sort(all(b), [](block &x, block &y) { return x.w + x.s < y.w + y.s; });

    vector<i64> dp(2e4 + 10);
    for (auto& [ w, s, v ] : b) {
        for (i64 i = s; i >= 0; i--) {
            dp[i + w] = max(dp[i + w], dp[i] + v);
        }
    }
    cout << *max_element(all(dp)) << endl;
}

int main() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    solve();
}

```