#include <bits/stdc++.h>

using namespace std;

const int maxn = 1e3+10;
const int maxs = 2e4+10;

int n;
long long int dp[maxn][maxs], w[maxn], s[maxn], v[maxn], d[maxn];

bool comp(int i, int j){
	return s[i] < s[j];
}

int main(){
	cin >> n;
	for (int i = 0; i < n; i++){
		scanf("%d%d%d", &w[i], &s[i], &v[i]);
		s[i] += w[i];
		d[i] = i;
	}

	sort(d, d+n, comp);

	for (int i = w[d[0]]; i < maxs; i++)
		dp[0][i] = v[d[0]];

	for (int i = 1; i < n; i++){
		for (int j = 0; j < maxs; j++){
			dp[i][j] = dp[i-1][j];
			if (w[d[i]] <= j){
				dp[i][j] = max(dp[i][j], dp[i-1][min(j-w[d[i]], s[d[i]]-w[d[i]])] + v[d[i]]);
			}
		}
	}

	cout << dp[n-1][maxs-1] << endl;
	return 0;
}

### Prompt

Your task is to create a cpp solution 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;

const int maxn = 1e3+10;
const int maxs = 2e4+10;

int n;
long long int dp[maxn][maxs], w[maxn], s[maxn], v[maxn], d[maxn];

bool comp(int i, int j){
	return s[i] < s[j];
}

int main(){
	cin >> n;
	for (int i = 0; i < n; i++){
		scanf("%d%d%d", &w[i], &s[i], &v[i]);
		s[i] += w[i];
		d[i] = i;
	}

	sort(d, d+n, comp);

	for (int i = w[d[0]]; i < maxs; i++)
		dp[0][i] = v[d[0]];

	for (int i = 1; i < n; i++){
		for (int j = 0; j < maxs; j++){
			dp[i][j] = dp[i-1][j];
			if (w[d[i]] <= j){
				dp[i][j] = max(dp[i][j], dp[i-1][min(j-w[d[i]], s[d[i]]-w[d[i]])] + v[d[i]]);
			}
		}
	}

	cout << dp[n-1][maxs-1] << endl;
	return 0;
}

```