Bob has $n$ sticks. The $i$-th stick has length $a_i$. He needs to choose a tuple of $4$ sticks ($i$, $j$, $k$, $p$) such that:

• $1 \leq i < j < k < p \leq n$;
• by moving and rotating the sticks any way you want (without breaking them) you can obtain a parallelogram with sides of lengths $a_i, a_j, a_k, a_p$.

Task

Bob is interested if there is such a tuple. He asks you to print YES if you can choose 4 sticks satisfying the above properties, and NO otherwise.

Input

The first line contains an integer $t$ ($1 \leq t \leq 10^4$) the number of test cases. Then follows the description of each test case.

The first line of each test case contains a single integer $n$ ($1 \leq n \leq 2 \cdot 10^5$) the number of sticks.

The second line of each test case contains $n$ integers $a_1, a_2, \dots a_n$ ($1 \leq a_i \leq n$) - the length of the sticks.

It is guaranteed that the sum of the values of $n$ over all test cases does not exceed $2 \cdot 10^5$.

Output

For each test case, you have to print the answer to Bob's question.

Examples

stdin

3
7
1 2 3 3 1 3 2
8
1 2 3 4 5 6 7 7
4
1 1 1 1

stdout

YES
NO
YES