//g++  5.4.0

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

#define ff first
#define ss second
#define int long long
#define pb push_back
#define pii pair< int,int >
#define fast ios::sync_with_stdio(0) , cin.tie(0) , cout.tie(0) ;

struct S
{
    int w,s,v;
    
    bool operator<(const S &b) const
    {
        return w+s < b.w+b.s;
    }
};
signed main()
{
    fast;
    int n;
    cin >> n;
    vector<S> ip(n);
    vector<int> dp(2e4+1,0);
    for(int i=0;i<n;i++)
    {
        cin >> ip[i].w >> ip[i].s >> ip[i].v;
    }
    sort( ip.begin() , ip.end() );
    for( auto p : ip )
    {
        for( int W = p.s ; W >= 0 ; W-- )
            dp[ W+p.w ] = max( dp[ W+p.w ] , dp[W] + p.v );
    }
    cout << *max_element( dp.begin() , dp.end() );
        
}




### 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
//g++  5.4.0

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

#define ff first
#define ss second
#define int long long
#define pb push_back
#define pii pair< int,int >
#define fast ios::sync_with_stdio(0) , cin.tie(0) , cout.tie(0) ;

struct S
{
    int w,s,v;
    
    bool operator<(const S &b) const
    {
        return w+s < b.w+b.s;
    }
};
signed main()
{
    fast;
    int n;
    cin >> n;
    vector<S> ip(n);
    vector<int> dp(2e4+1,0);
    for(int i=0;i<n;i++)
    {
        cin >> ip[i].w >> ip[i].s >> ip[i].v;
    }
    sort( ip.begin() , ip.end() );
    for( auto p : ip )
    {
        for( int W = p.s ; W >= 0 ; W-- )
            dp[ W+p.w ] = max( dp[ W+p.w ] , dp[W] + p.v );
    }
    cout << *max_element( dp.begin() , dp.end() );
        
}




```