#include <bits/stdc++.h>
#define MX 20000
using namespace std;
typedef long long lnt;
template <class T> inline void read(T &x) {
	x = 0; int c = getchar(), f = 1;
	for (; !isdigit(c); c = getchar()) if (c == 45) f = -1;
	for (; isdigit(c); c = getchar()) (x *= 10) += f*(c-'0');
}
int n; lnt f[MX+5], mx;
struct node {int w, s, v;} a[1005];
bool cmp(const node &x, const node &y) {return x.w+x.s < y.w+y.s;}
int main() {
	read(n);
	for (int i = 1; i <= n; i++)
		read(a[i].w), read(a[i].s), read(a[i].v);
	sort(a+1, a+n+1, cmp);
	for (int i = 1; i <= n; i++)
		for (int j = min(a[i].s+a[i].w, MX); j >= a[i].w; j--)
			f[j] = max(f[j], f[j-a[i].w]+a[i].v), mx = max(mx, f[j]);
	return printf("%lld\n", mx), 0;
}

### Prompt

Please formulate 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>
#define MX 20000
using namespace std;
typedef long long lnt;
template <class T> inline void read(T &x) {
	x = 0; int c = getchar(), f = 1;
	for (; !isdigit(c); c = getchar()) if (c == 45) f = -1;
	for (; isdigit(c); c = getchar()) (x *= 10) += f*(c-'0');
}
int n; lnt f[MX+5], mx;
struct node {int w, s, v;} a[1005];
bool cmp(const node &x, const node &y) {return x.w+x.s < y.w+y.s;}
int main() {
	read(n);
	for (int i = 1; i <= n; i++)
		read(a[i].w), read(a[i].s), read(a[i].v);
	sort(a+1, a+n+1, cmp);
	for (int i = 1; i <= n; i++)
		for (int j = min(a[i].s+a[i].w, MX); j >= a[i].w; j--)
			f[j] = max(f[j], f[j-a[i].w]+a[i].v), mx = max(mx, f[j]);
	return printf("%lld\n", mx), 0;
}

```