Evaluate RBS

Description:

Input:

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 1500$$$) — the number of testcases.

The first line of each testcase contains a single integer $$$n$$$ ($$$1 \le n \le 1500$$$).

The $$$i$$$-th of the next $$$2n$$$ lines contains two integers $$$a_i$$$ and $$$b_i$$$ ($$$1 \le a_i, b_i \le 10^6$$$) and a character $$$c_i$$$ ($$$c_i = $$$'(' or $$$c_i = $$$')'). Exactly $$$n$$$ tuples have $$$c_i = $$$'(' and the other $$$n$$$ tuples have $$$c_i =$$$ ')'.

The sum of $$$n$$$ over all testcases doesn't exceed $$$1500$$$.

Output:

For each testcase, print "YES" if it's possible to choose such $$$x$$$ and $$$y$$$ that taking brackets $$$c$$$ from the tuples in the resulting order produces a regular bracket sequence. Otherwise, print "NO".

Sample Input:

4
1
1 4 (
2 3 )
1
1 2 )
3 4 (
4
16 5 (
12 3 (
19 6 )
4 10 )
3 10 )
19 11 (
19 7 )
7 14 (
4
16 8 (
11 9 )
20 10 )
20 19 )
2 13 (
18 7 (
15 19 )
5 6 (

Sample Output:

YES
NO
NO
YES

Note:

In the first testcase, you can choose $$$x = 10, y = 0.1$$$. The values for tuples will be $$$10 \cdot 1 + 0.1 \cdot 4 = 10.4$$$ and $$$10 \cdot 2 + 0.1 \cdot 3 = 20.3$$$. Thus, the first tuple will go first, then the second one, making the bracket sequence "()", which is regular.

In the second testcase, you can't choose positive $$$x$$$ and $$$y$$$ such that the opening brackets gets assigned a value less or equal to the value of the closing bracket.

In the fourth testcase, you can choose $$$x = 0.6, y = 0.55$$$. The bracket sequence is "(()(()))".