- Given an array
**arr[]**of**N**distinct integers, check if this array is Sorted and Rotated clockwise.

A sorted array is not considered as sorted and rotated, i.e., there should be at least one rotation.

Note:-Array can be sorted both increasingly and decreasingly

Input

The first line of input contains number of testcases T. Each testcase contains 2 lines, the first line contains N, the number of elements in array, and second line contains N space separated elements of array.

**Constraints:**

1 <= T <= 50

3 <= N <= 10^3

1 <= A[i] <= 10^4

Output

Print “**Yes**” if the given array is sorted and rotated, else Print “**No**”, without Inverted commas.

Example

Sample Input:

2

4

3 4 1 2

3

1 3 2

Sample Output:

Yes

Yes

- Given an integer K, find a positive integer x such that
**K = x2 + 3*x**. If no such positive integer x exists, print -1.

Input

First and the only line of the input contains an integer K.

Constraints:

1 <= K <= 1018

Output

Print a positive integer x such that the above equation satisfies. If no such integer x exists, print -1.