You are given $$$2n$$$ tuples of values $$$(a, b, c)$$$, where $$$a$$$ and $$$b$$$ are positive integers and $$$c$$$ is a bracket '(' or ')'. Exactly $$$n$$$ tuples have $$$c = $$$'(' and the other $$$n$$$ tuples have $$$c =$$$ ')'.

You are asked to choose two positive values $$$x$$$ and $$$y$$$ ($$$x \gt 0$$$ and $$$y \gt 0$$$; not necessarily integers) and sort the tuples in the increasing value of $$$a \cdot x + b \cdot y$$$. If several tuples have the same value, you can place them in any order among themselves.

Is it possible to choose such $$$x$$$ and $$$y$$$ that taking brackets $$$c$$$ from the tuples in the resulting order produces a regular bracket sequence?

A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters "1" and "+" between the original characters of the sequence.

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".

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 "(()(()))".

Evaluate RBS

Examples