collectmushrooms4

Problem Description

Gug is collecting mushrooms again. This time he is collecting it in linear land, where there are N houses arranged in a row. Getting a permit to dig mushrooms in front of house i costs C_i dollars, but once it is bought, Gug can direct as many minions as he wants to dig mushrooms there. Gug has M minions. Minion i wants to pick mushrooms between houses S_i and E_i, and will gain H_i dollars if it is allowed to do so. Help Gug decide a subset of minions to allow to pick mushrooms such that he gains the most amount of money.

Input

The first line of input will contain two integers, N and M.

The second line of input will contain N integers, representing the array C.

The next M lines of input will contain three integers each, S_i, E_i and H_i.

Output

The output should contain one integer, the maximum net profit Gug can gain.

Limits

For all subtasks: 0 ≤ S_i, E_i < N, 0 ≤ H_i, C_i ≤ 10⁹.

Subtask 1 (10%): 1 ≤ N ≤ 500, 1 ≤ M ≤ 15.

Subtask 2 (12%): 1 ≤ N ≤ 2000, 1 ≤ M ≤ 20.

Subtask 3 (30%): 1 ≤ N ≤ 200, 1 ≤ M ≤ 200.

Subtask 4 (22%): 1 ≤ N ≤ 1000, 1 ≤ M ≤ 2000.

Subtask 5 (26%): 1 ≤ N ≤ 300000, 1 ≤ M ≤ 300000.

Subtask 6 (0%): Sample Testcases.

Sample Input 1

2 1
0 3
0 1 5

Sample Output 1

2

Sample Input 2

7 4
3 2 3 2 1 2 3
0 1 5
1 2 5
2 4 3
6 6 5

Sample Output 2

4