Erine has a sequence $a$ of length $n$. Clearly, this sequence has $2^n-1$ non-empty subsequences (if two subsequences have the same content but different positions, we consider them as two distinct subsequences).

Erine writes all $2^n-1$ subsequences on a piece of paper. After writing them down, she wants to organize and categorize these subsequences. Specifically, Erine puts subsequences with the same content into the same box, while subsequences with different contents are placed in different boxes.

However, there are too many subsequences! Erine only wants to know whether, after organizing the subsequences, every non-empty box contains exactly an odd number of subsequences.

Input

This problem contains multiple test cases.

The first line contains an integer $t$ ($1 \leq t \leq 10^5$), representing the number of test cases. For each test case:

• The first line contains an integer $n$ ($1 \le n \le 2\times 10^6$).
• The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le n$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2\times 10^6$.

Output

For each test case, output a single line containing the string Yes or No, indicating whether every non-empty box contains exactly an odd number of subsequences after organizing them.

Examples

Input 1

3
3
1 2 1
5
1 1 1 2 3
7
2 2 2 2 2 2 2

Output 1

No
Yes
Yes

Note

For the first test case, the box containing the subsequence $\{1\}$ has $2$ subsequences.

For the second test case, every non-empty box contains exactly an odd number of subsequences.