Score : 500 points

Problem Statement

We have N camels numbered 1,2,\ldots,N. Snuke has decided to make them line up in a row.

The happiness of Camel i will be L_i if it is among the K_i frontmost camels, and R_i otherwise.

Snuke wants to maximize the total happiness of the camels. Find the maximum possible total happiness of the camel.

Solve this problem for each of the T test cases given.

Constraints

  • All values in input are integers.
  • 1 \leq T \leq 10^5
  • 1 \leq N \leq 2 \times 10^{5}
  • 1 \leq K_i \leq N
  • 1 \leq L_i, R_i \leq 10^9
  • The sum of values of N in each input file is at most 2 \times 10^5.

Input

Input is given from Standard Input in the following format:

T
\mathrm{case}_1
\vdots
\mathrm{case}_T

Each case is given in the following format:

N
K_1 L_1 R_1
\vdots
K_N L_N R_N

Output

Print T lines. The i-th line should contain the answer to the i-th test case.

Sample Input 1

3
2
1 5 10
2 15 5
3
2 93 78
1 71 59
3 57 96
19
19 23 16
5 90 13
12 85 70
19 67 78
12 16 60
18 48 28
5 4 24
12 97 97
4 57 87
19 91 74
18 100 76
7 86 46
9 100 57
3 76 73
6 84 93
1 6 84
11 75 94
19 15 3
12 11 34

Sample Output 1

25
221
1354
  • In the first test case, it is optimal to line up the camels in the order 2, 1.
    • Camel 1 is not the frontmost camel, so its happiness will be 10.
    • Camel 2 is among the two frontmost camels, so its happiness will be 15.
  • In the second test case, it is optimal to line up the camels in the order 2, 1, 3.
    • Camel 1 is among the two frontmost camels, so its happiness will be 93.
    • Camel 2 is the frontmost camel, so its happiness will be 71.
    • Camel 3 is among the three frontmost camels, so its happiness will be 57.