Let $x_1,x_2,x_3,\dots$ be variables. $n$ constraints of form $x_i=x_j$ or $x_i\ne x_j$ are given. The task asks for whether it is possible to assign values to the variables so that all constraints can be satisfied. For example, if the constraints are $x_1=x_2,x_2=x_3,x_3=x_4,x_1\ne x_4$, then those constraints cannot be satisfied simultaneously.

Input Specification

The first line of the input is an integer $t$ representing the number of instances to solve. The instances are independent. For each instance, the first line is an integer $n$ representing the number of constraints to be satisfied. In the following $n$ lines, each line has three integers $i,j,e$ representing an equality/inequality constraint. If $e=1$, the constraint shall be $x_i=x_j$. If $e=0$, the constraint shall be $x_i\ne x_j$.

Output Specification

The output has $t$ lines. The $k$-th line of the output is a string YES or NO. Output YES if the constraints in that instance can be satisfied and NO otherwise.

Sample Input 1

2
2
1 2 1
1 2 0
2
1 2 1
2 1 1

Sample Output 1

NO
YES

Sample Input 2

2
3
1 2 1
2 3 1
3 1 1
4
1 2 1
2 3 1
3 4 1
1 4 0

Sample Output 2

YES
NO

Constraints

Test Case	$n$	$i,j$	Additional Constraints
1	$1\le n\le 10$	$1\le i,j\le 10000$	$1\le t\le 10$ $e\in \{0,1\}$
2
3	$1\le n\le 100$
4
5	$1\le n\le 100000$
6
7
8	$1\le n\le 100000$	$1\le i,j\le 1000000000$
9
10