2437 - Pattern Finder Oceania - South Pacific - 2008/2009
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A number pattern is a sequence of two or more numbers that satisfies a certain rule. For instance, the sequence `` 3, 5, 7, 9,... " is a number pattern that starts with three and jumps by twos. In primary school, number patterns are used as a tool for learning basic arithmetic and problem-solving skills. Finding a number pattern in a grid of integers is Mrs Brown's favourite challenge for her pupils.

Mrs Brown's number pattern challenge for her 2^nd grade pupils is to find a number pattern in a grid of integers. The number pattern must start at the smallest value, jumps to an adjacent cell in the grid by adding a fixed positive value, and terminates at the largest value. Two cells are considered adjacent if they share the same row or share the same column.

For instance, the grid on the left has a pattern that starts at 4 and jumps by 2 and terminates at the largest value of 14, but no pattern can be found in the grid on the right.

Mrs Brown has a large number of these grids, but she does not have the time to find the correct answer for each one. Your task is to help by writing a program to check the existence of a pattern of the required form in a given grid.

Input 

The input consists of a series of scenarios. The first line in each scenario consists of two positive integers N and M that represent the number of rows and columns in a grid. 1N, M100 . Each of the following N lines contains M integers that represent the integers in a single row in the grid. The integers are separated by single spaces, and have values that does not exceed 30000.

Input is terminated by a challenge where N and M equal -1.

This challenge should not be processed.

Output 

Output consists of one line for each grid. It will be in one of the following two formats:

At least one pattern exists.
No pattern can be found.

Sample Input 

28 
77 78 79 77 77 77 77 77 
78 79 80 81 82 83 84 85 
-1 -1

Sample Output 

At least one pattern exists.