#include<bits/stdc++.h>
using namespace std;
using ll = int64_t;
using P = pair<ll, ll>;

const ll INF = 5e15;
const ll MOD = 1e9 + 7;

struct B {
    ll w, s, v;
};

vector<ll> dp(2 * 1e4 + 10);

int main(){
    ll N;
    cin >> N;
    vector<B> V(N);
    for(auto &e : V) cin >> e.w >> e.s >> e.v;
    sort(V.begin(), V.end(), [](const B &a, const B &b){ return a.w + a.s < b.w + b.s; });
    for(const B &e : V){
        auto tmp = dp;
        for(ll W = 0; W + e.w < dp.size() && W <= e.s; W++) tmp[W + e.w] = max(tmp[W + e.w], dp[W] + e.v);
        dp = move(tmp);
    }
    cout << *max_element(dp.begin(), dp.end()) << endl;
    return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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;
using ll = int64_t;
using P = pair<ll, ll>;

const ll INF = 5e15;
const ll MOD = 1e9 + 7;

struct B {
    ll w, s, v;
};

vector<ll> dp(2 * 1e4 + 10);

int main(){
    ll N;
    cin >> N;
    vector<B> V(N);
    for(auto &e : V) cin >> e.w >> e.s >> e.v;
    sort(V.begin(), V.end(), [](const B &a, const B &b){ return a.w + a.s < b.w + b.s; });
    for(const B &e : V){
        auto tmp = dp;
        for(ll W = 0; W + e.w < dp.size() && W <= e.s; W++) tmp[W + e.w] = max(tmp[W + e.w], dp[W] + e.v);
        dp = move(tmp);
    }
    cout << *max_element(dp.begin(), dp.end()) << endl;
    return 0;
}

```