#include <bits/stdc++.h>
using namespace std;
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n)   FOR(i,0,n)
#define pb emplace_back
typedef long long ll;
typedef pair<int,int> pint;

int n;
ll v[1001],w[1001],s[1001];
ll dp[1001][20022];
int ord[1001];
bool cmp(const int& l,const int& r){
    return min(s[l],s[r]-w[l])>min(s[r],s[l]-w[r]);
}
int main(){
    cin>>n;
    rep(i,n) cin>>w[i]>>s[i]>>v[i];
    rep(i,n) ord[i]=i;
    sort(ord,ord+n,cmp);
    rep(i,n)rep(j,20002){
        int id=ord[i];
        dp[i+1][j]=max(dp[i+1][j],dp[i][j]);
        if(j<=s[id]) dp[i+1][j+w[id]]=max(dp[i+1][j+w[id]],dp[i][j]+v[id]);
    }
    ll ans=0;
    rep(i,20002) ans=max(ans,dp[n][i]);
    cout<<ans<<endl;
    return 0;
}

### Prompt

Create a solution in cpp for 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 FOR(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n)   FOR(i,0,n)
#define pb emplace_back
typedef long long ll;
typedef pair<int,int> pint;

int n;
ll v[1001],w[1001],s[1001];
ll dp[1001][20022];
int ord[1001];
bool cmp(const int& l,const int& r){
    return min(s[l],s[r]-w[l])>min(s[r],s[l]-w[r]);
}
int main(){
    cin>>n;
    rep(i,n) cin>>w[i]>>s[i]>>v[i];
    rep(i,n) ord[i]=i;
    sort(ord,ord+n,cmp);
    rep(i,n)rep(j,20002){
        int id=ord[i];
        dp[i+1][j]=max(dp[i+1][j],dp[i][j]);
        if(j<=s[id]) dp[i+1][j+w[id]]=max(dp[i+1][j+w[id]],dp[i][j]+v[id]);
    }
    ll ans=0;
    rep(i,20002) ans=max(ans,dp[n][i]);
    cout<<ans<<endl;
    return 0;
}

```