A Ducci sequence is a sequence of n-tuples of integers. Given an n-tuple of integers (a1, a2, · · · , an), the next n-tuple in the sequence is formed by taking the absolute differences of neighboring integers:

                                                                                 (a1, a2, · · · , an) → (|a1 − a2|, |a2 − a3|, · · · , |an − a1|)

      Ducci sequences either reach a tuple of zeros or fall into a periodic loop. For example, the 4-tuple sequence starting with 8,11,2,7 takes 5 steps to reach the zeros tuple:

                                                     (8, 11, 2, 7) → (3, 9, 5, 1) → (6, 4, 4, 2) → (2, 0, 2, 4) → (2, 2, 2, 2) → (0, 0, 0, 0).

      The 5-tuple sequence starting with 4,2,0,2,0 enters a loop after 2 steps:

                              (4, 2, 0, 2, 0) → (2, 2, 2, 2, 4) → (0,0,0,2,2) → (0, 0, 2, 0, 2) → (0, 2, 2, 2, 2) → (2, 0, 0, 0, 2) → (2, 0, 0, 2, 0) →

                            (2, 0, 2, 2, 2) → (2, 2, 0, 0, 0) → (0, 2, 0, 0, 2) → (2, 2, 0, 2, 2) → (0, 2, 2, 0, 0) → (2, 0, 2, 0, 0) → (2, 2, 2, 0, 2) →

                                                                   (0, 0, 2, 2, 0) → (0, 2, 0, 2, 0) → (2, 2, 2, 2, 0) → (0,0,0,2,2) → · · ·

      Given an n-tuple of integers, write a program to decide if the sequence is reaching to a zeros tuple or a periodic loop.

Input

Your program is to read the input from standard input. The input consists of T test cases. The number of test cases T is given in the first line of the input. Each test case starts with a line containing an integer n (3 ≤ n ≤ 15), which represents the size of a tuple in the Ducci sequences. In the following line, n integers are given which represents the n-tuple of integers. The range of integers are from 0 to 1,000. You may assume that the maximum number of steps of a Ducci sequence reaching zeros tuple or making a loop does not exceed 1,000. Output Your program is to write to standard

output.

Print exactly one line for each test case. Print ‘LOOP’ if the Ducci sequence falls into a periodic loop, print ‘ZERO’ if the Ducci sequence reaches to a zeros tuple.

Sample Input

4

4

8 11 2 7

5

4 2 0 2 0

7

0 0 0 0 0 0 0

6 1 2 3 1 2 3

Sample Output

ZERO

LOOP

ZERO

LOOP

好水的题，，直接莽过去就行了过了，，，或许有不需要循环这么多次的方法。。。

 

1 #include 
     
       2 #include 
      
        3 #include 
       
         4 using namespace std; 5 int a[20]; 6 int n; 7 bool change()  //模拟运算过程 8 { 9     int sum = 0;10     int t = a[1];11     for(int i = 1; i <= n;i++)12     {13         if(i!=n) a[i] = abs(a[i]-a[i+1]);14         else a[i] = abs(a[i]-t);15         sum+=a[i];16     }17     if(sum==0) return true;18     else return false;19 }20 int main()21 {22     int T;23     scanf("%d",&T);24     while(T--)25     {26         scanf("%d",&n);27         for(int i = 1;i <= n;i++)28         {29             scanf("%d",&a[i]);30         }31         int j;32         for( j = 1;j <= 1000 ; j++)33         {34             if(change()) break;35         }36         if(j>1000) printf("LOOP\n");37         else printf("ZERO\n");38     }39     return 0;40 }