Problem:
Score : 100 points

Problem Statement

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.

Sample Input 1

3
2 2 20
2 1 30
3 1 40

Sample Output 1

50

If Blocks 2, 1 are stacked in this order from top to bottom, this tower will satisfy the condition, with the total value of 30 + 20 = 50.

Sample Input 2

4
1 2 10
3 1 10
2 4 10
1 6 10

Sample Output 2

40

Blocks 1, 2, 3, 4 should be stacked in this order from top to bottom.

Sample Input 3

5
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000

Sample Output 3

5000000000

The answer may not fit into a 32-bit integer type.

Sample Input 4

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

Sample Output 4

22

We should, for example, stack Blocks 5, 6, 8, 4 in this order from top to bottom.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <algorithm>
#include <cstdint>
#include <cstring>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>

using namespace std;
#define REP(i, n) for (int i = 0; i < n; i++)
#define FOR(i, s, t) for (int i = s; i < t; i++)
#define ALL(obj) obj.begin(), obj.end()

const int iINF = 1e9;
const long long llINF = 1e18;
const int MOD = 1e9 + 7;
template <class T>
inline bool chmax(T& a, T b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
inline bool chmin(T& a, T b) {
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}

template <int MOD>
struct ModInt {
    long long val;
    constexpr ModInt(long long v = 0) noexcept : val(v % MOD) {
        if (val < 0) val += MOD;
    }
    constexpr int getmod() { return MOD; }
    constexpr ModInt operator-() const noexcept { return val ? MOD - val : 0; }
    constexpr ModInt operator+(const ModInt& r) const noexcept { return ModInt(*this) += r; }
    constexpr ModInt operator-(const ModInt& r) const noexcept { return ModInt(*this) -= r; }
    constexpr ModInt operator*(const ModInt& r) const noexcept { return ModInt(*this) *= r; }
    constexpr ModInt operator/(const ModInt& r) const noexcept { return ModInt(*this) /= r; }
    constexpr ModInt& operator+=(const ModInt& r) noexcept {
        val += r.val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    constexpr ModInt& operator-=(const ModInt& r) noexcept {
        val -= r.val;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr ModInt& operator*=(const ModInt& r) noexcept {
        val = val * r.val % MOD;
        return *this;
    }
    constexpr ModInt& operator/=(const ModInt& r) noexcept {
        long long a = r.val, b = MOD, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b;
            swap(a, b);
            u -= t * v;
            swap(u, v);
        }
        val = val * u % MOD;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr bool operator==(const ModInt& r) const noexcept { return this->val == r.val; }
    constexpr bool operator!=(const ModInt& r) const noexcept { return this->val != r.val; }
    friend constexpr ostream& operator<<(ostream& os, const ModInt<MOD>& x) noexcept { return os << x.val; }

    friend constexpr istream& operator>>(istream& is, ModInt<MOD>& x) noexcept { return is >> x.val; }
    friend constexpr ModInt<MOD> modpow(const ModInt<MOD>& a, long long n) noexcept {
        if (n == 0) return 1;
        auto t = modpow(a, n / 2);
        t = t * t;
        if (n & 1) t = t * a;
        return t;
    }
};

using mint = ModInt<MOD>;

long long modPow(long long x, long long n, long long mod) {
    long long res = 1;
    while (n > 0) {
        if (n & 1) res = res * x % mod;
        x = x * x % mod;
        n >>= 1;
    }
    return res;
}

long long extGCD(long long a, long long b, long long& x, long long& y) {
    if (b == 0) {
        x = 1;
        y = 0;
        return a;
    }

    long long d = extGCD(b, a % b, y, x);
    y -= a / b * x;
    return d;
}

long long gcd(long long a, long long b) {
    if (b == 0) {
        return a;
    } else {
        return gcd(b, a % b);
    }
}

long long lcm(long long a, long long b) { return a / gcd(a, b) * b; }

template <typename T>
map<T, int> compress(vector<T> x) {
    map<T, int> res;
    sort(x.begin(), x.end());
    x.erase(unique(x.begin(), x.end()), x.end());
    for (int i = 0; i < x.size(); i++) {
        res[x[i]] = i;
    }

    return res;
}

template <typename T>
int former(const vector<T>& v, T x) {
    return upper_bound(v.begin(), v.end(), x) - v.begin() - 1;
}

template <typename T>
int latter(const vector<T>& v, T x) {
    return lower_bound(v.begin(), v.end(), x) - v.begin();
}

template <typename T>
using Vec = vector<T>;
template <typename T>
using VVec = vector<vector<T>>;
using LL = long long;

LL dp[1010][10010];
int main() {
    int N;
    cin >> N;
    Vec<int> w(N), s(N);
    Vec<LL> v(N);
    REP(i, N) cin >> w[i] >> s[i] >> v[i];
    int S = *max_element(ALL(s));
    Vec<int> ord;
    REP(i, N) ord.push_back(i);
    sort(ALL(ord), [&](int a, int b) { return min(s[a], s[b] - w[a]) > min(s[b], s[a] - w[b]); });
    REP(i, N) {
        REP(j, S + 1) {
           int a = ord[i];
            chmax(dp[i + 1][j], dp[i][j]);
            if (j <= s[a]) chmax(dp[i + 1][min(j + w[a], S + 1)], dp[i][j] + v[a]);
        }
        chmax(dp[i + 1][S + 1], dp[i][S + 1]);
    }
    LL ans = 0;
    REP(i, S + 2) chmax(ans, dp[N][i]);
    cout << ans << endl;
}