2465: Series 2

Let A be an integral series {A₁, A₂, . . . , A_n}. 

The zero-order series of A is A itself.

The first-order series of A is {B₁, B₂, . . . , B_n-1, where B_i = A_i+1 - A_i.

The ith-order series of A is the first-order series of its (i - 1)th-order series (2<=i<=n - 1).

We say A is monotonic iff A₁<=A₂<=. . . <=A_n or A₁>= A₂ >=. . . >= A_n.

A is kth-order monotonic iff all ith-order series (0<=i<=k) are monotonic, and (k + 1)th-order are not.

Specially, if the zero-order series of A is not monotonic, then A is named ugly series. If all ith-order (0<=i<=n - 1) series of A are monotonic, then A is a nice series.

Given A, determine whether it’s a ugly series or nice series. If both are not, determine k.

The input consists of several test cases. The first line of input gives the number of test cases T (T<=50).

For each test case:
The first line contains a single integer n(1<=n<=10⁵), which denotes the length of series A.
The second line consists of n integers, describing A₁, A₂, . . . , A_n. (0<=|A_i|<=2⁶⁰)

For each test case, output either ugly series, nice series or a single integer k.

4
3
1 3 2
4
1 4 6 7
4
1 3 4 7
5
-1 0 3 11 29

ugly series 
nice series 
0
nice series