p02610 AIsing Programming Contest 2020 - Camel Train
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.

Example

Input

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


Output

25
221
1354
```python
import sys
from heapq import heappush, heappop
from operator import itemgetter

sys.setrecursionlimit(10 ** 7)
rl = sys.stdin.readline


def solve():
    N = int(rl())
    res = 0
    camel_left, camel_right = [], []
    for _ in range(N):
        K, L, R = map(int, rl().split())
        res += min(L, R)
        if R <= L:
            camel_left.append([K, L, R])
        elif K != N:
            camel_right.append([N - K, L, R])
    
    camel_left.sort(key=itemgetter(0))
    camel_right.sort(key=itemgetter(0))
    
    hq = []
    i = 0
    for j in range(1, N + 1):
        while i < len(camel_left) and camel_left[i][0] == j:
            heappush(hq, camel_left[i][1] - camel_left[i][2])
            i += 1
        while j < len(hq):
            heappop(hq)
    res += sum(hq)
    
    hq = []
    i = 0
    for j in range(1, N):
        while i < len(camel_right) and camel_right[i][0] == j:
            heappush(hq, camel_right[i][2] - camel_right[i][1])
            i += 1
        while j < len(hq):
            heappop(hq)
    res += sum(hq)
    
    return res


if __name__ == '__main__':
    T = int(rl())
    ans = []
    for _ in range(T):
        ans.append(solve())
    print(*ans, sep='\n')

```