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C. Dominated Subarray
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Let's call an array $$$t$$$ dominated by value $$$v$$$ in the next situation.

At first, array $$$t$$$ should have at least $$$2$$$ elements. Now, let's calculate number of occurrences of each number $$$num$$$ in $$$t$$$ and define it as $$$occ(num)$$$. Then $$$t$$$ is dominated (by $$$v$$$) if (and only if) $$$occ(v) > occ(v')$$$ for any other number $$$v'$$$. For example, arrays $$$[1, 2, 3, 4, 5, 2]$$$, $$$[11, 11]$$$ and $$$[3, 2, 3, 2, 3]$$$ are dominated (by $$$2$$$, $$$11$$$ and $$$3$$$ respectevitely) but arrays $$$[3]$$$, $$$[1, 2]$$$ and $$$[3, 3, 2, 2, 1]$$$ are not.

Small remark: since any array can be dominated only by one number, we can not specify this number and just say that array is either dominated or not.

You are given array $$$a_1, a_2, \dots, a_n$$$. Calculate its shortest dominated subarray or say that there are no such subarrays.

The subarray of $$$a$$$ is a contiguous part of the array $$$a$$$, i. e. the array $$$a_i, a_{i + 1}, \dots, a_j$$$ for some $$$1 \le i \le j \le n$$$.

Input

The first line contains single integer $$$T$$$ ($$$1 \le T \le 1000$$$) — the number of test cases. Each test case consists of two lines.

The first line contains single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the length of the array $$$a$$$.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le n$$$) — the corresponding values of the array $$$a$$$.

It's guaranteed that the total length of all arrays in one test doesn't exceed $$$2 \cdot 10^5$$$.

Output

Print $$$T$$$ integers — one per test case. For each test case print the only integer — the length of the shortest dominated subarray, or $$$-1$$$ if there are no such subarrays.

Example
Input
4
1
1
6
1 2 3 4 5 1
9
4 1 2 4 5 4 3 2 1
4
3 3 3 3
Output
-1
6
3
2
Note

In the first test case, there are no subarrays of length at least $$$2$$$, so the answer is $$$-1$$$.

In the second test case, the whole array is dominated (by $$$1$$$) and it's the only dominated subarray.

In the third test case, the subarray $$$a_4, a_5, a_6$$$ is the shortest dominated subarray.

In the fourth test case, all subarrays of length more than one are dominated.