Unique ID#11853

Unique ID

1 second

256 megabytes

Easy

"Free HyperCharge !"

—Brawl Stars Fan

Yamen is enjoying having toys, cats, dogs, and other funny things to do in his own room. But ... when things turn out into mess , everything should be arranged ! Therefore, Yamen decided to give a unique enumeration for each of his stuff. According to Yamen, everything is balanced if and only if everything that he owns has a unique ID , and every ID is used only for exactly one thing. Yamen was very confused, worrying about the balance of items , so he may accidentally repeat some of them in the list.

Yamin considers everything to be balanced if and only if , each item name in the list corresponds to single integer and each integer in the list corresponds to single item name.

And since Yamin is confused , He may have repeated some of them in the list. Determine if everything is balanced.

Input

The first line contains a single $t$ $(1 \leq t \leq 100)$ (1 \le t \le 100) – the number of test cases.

The first line of each test case contains a single integer $n$ $(1 \leq n \leq 4 \cdot 1 0^{5})$ (1 \le n \le 4 \cdot 10^5) – the number of items Yamen has.

The next $n$ lines have two values string $a_{i}$ a_i and integer $b_{i}$ b_i $(a_{i}, b_{i})$ (a_i,b_i) , $(1 \leq ∣ a_{i} ∣ \leq 5; 1 \leq b_{i} \leq 1 0^{6})$ (1 \le |a_i| \le 5 ; 1 \le b_i \le 10^6) where $a_{i}$ a_i represents the name of the item consisting of only lowercase English characters and $b_{i}$ b_i represents its own ID.

Pairs $(a_{i}, b_{i})$ (a_i,b_i) are not necessarily distinct for the single list of items

It's guaranteed that the sum of $n$ overall tests doesn't exceed $4 \cdot 1 0^{5}$ 4 \cdot 10^5.

Output

For each test case, if everything is Balanced, print "YES"; otherwise, print "NO".

You can output the answer in any case (for example, the strings "yEs", "yes", "Yes", and "YeS" will be recognized as positive responses).

Examples

Example 1

Note

In the first test case , every item of $cat, dog, brawl$ \mathtt{cat,dog,brawl} appeared once and every number appeared only once , so it's Balanced.

In the second test case , $cat$ appeared twice but with the same ID, so it's correct , but for $dog$ it's two ID's $3$ and $4$ , thus it's not Balanced.

In the third test case , everything is Balanced.

In the fourth test case , ID $1$ has two items $abc, xyz$ , so it's not Balanced.

In the fifth test , everything is Balanced.

In the sixth test , everything is Balanced since Yamin repeated some of the list items.

Scoring

Subtask $1$ ( $5$ points) : $(1 \leq n \leq 3; 1 \leq b_{i} \leq 4)$ (1 \le n \le 3; 1\le b_i \le 4)
Subtask $2$ ( $5$ points) : $(1 \leq n \leq 50)$ (1 \le n \le 50).
Subtask $3$ ( $10$ points) : $(1 \leq n \leq 1000)$ (1 \le n \le 1000) + It's guaranteed that every $a_{i}$ a_i is distinct.
Subtask $4$ ( $10$ points) : $(1 \leq n \leq 1000)$ (1 \le n \le 1000) + It's guaranteed that every $b_{i}$ b_i is distinct.
Subtask $5$ ( $20$ points) : No additional constraints