Maximum Project Rewards

Each project is [start_day, end_day, reward]. It occupies every day from start_day through end_day, including both endpoints. You can participate in only one project on a day. Choose a subset with the largest total reward. A project starting on another project’s end day conflicts with it.

Implement project_rewards(projects).

Input

projects: Rows of three integers: start day, end day, and reward.

Output

Return the maximum total reward; the chosen projects need not be returned.

Constraints

1 ≤ projects ≤ 200,000. 1 ≤ start_day ≤ end_day ≤ 1,000,000,000. Rewards are positive integers at most 1,000,000,000.

Examples

Input:
projects = [
    [1, 2, 4],
    [3, 4, 5],
    [2, 3, 10]
]

Expected output:
expected = 10

Input:
std::vector<std::vector<long long>> projects = {
    {1, 2, 4},
    {3, 4, 5},
    {2, 3, 10}
};

Expected output:
long long expected = 10;

Input:
long[][] projects = new long[][] {
    new long[] {1, 2, 4},
    new long[] {3, 4, 5},
    new long[] {2, 3, 10}
};

Expected output:
long expected = 10;

Input:
projects = [
    [1, 2, 4],
    [2, 3, 5]
]

Expected output:
expected = 5

Input:
std::vector<std::vector<long long>> projects = {
    {1, 2, 4},
    {2, 3, 5}
};

Expected output:
long long expected = 5;

Input:
long[][] projects = new long[][] {
    new long[] {1, 2, 4},
    new long[] {2, 3, 5}
};

Expected output:
long expected = 5;

References

This challenge is adapted for CodeUtility. Follow the statement and constraints above.

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