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Series 2

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 262144/262144 K (Java/Others)
Total Submission(s): 875    Accepted Submission(s): 285


Problem Description
Let A be an integral series {A1, A2, . . . , An}.

The zero-order series of A is A itself.

The first-order series of A is {B1, B2, . . . , Bn-1, where Bi = Ai+1 - Ai.

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<=. . . <=An or A1>= A2 >=. . . >= An.

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.
 

Input
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, . . . , An. (0<=|Ai|<=260)
 

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

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

Sample Output
ugly series nice series 0 nice series
 

Author
BUPT
 

Source
 

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