An Arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2.

Given an unsorted array, find if it can be reordered to form an arithmetic sequence.

Examples

Array: [9, 13, 5, 15, 7, 11]
Answer: true
Explanation: This can be reordered to [5, 7, 9, 11, 13, 15] or [15, 13, 11, 9, 7, 5] both of which are arithmetic sequences.

Array: [1, 1, 1]
Answer: true
Explanation: This is an arithmetic sequence with a difference 0.

Array: [4, 1, 2]
Answer: false
Explanation: This cannot be reordered to form an arithmetic sequence.

Testing

Input Format

The first line contains 'T' denoting the no. of test cases.

Next T lines each contain a number 'n' denoting the number of elements, followed by n space-separated numbers denoting the array elements.

Output Format

T lines each contain true or false denoting whether the array for that test case can be used to form an arithmetic sequence.

Sample Input

3
6 9 13 5 15 7 11
3 1 1 1
3 4 1 2

Expected Output

true
true
false

Constraints

0 <= T <= 100

1 <= N <= 1000

-107 <= value of array element <= 107